A First Course in Differential Equations with Modeling Applications (11th Edition)

Chapter 8

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This is the matrix form of linear system. more

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; If the matrix represents the dependent ... more

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Step 1: Step 2: Step 3: Step 4: more

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Here we want to rewrite the given linear system ... more

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and ; Multiply the matrices of the equation and ... more

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Write the differential equations and in the ... more

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Differentiate with respect to to find .... more

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Differentiate with respect to to find Substitute... more

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Differentiate with respect to to find .... more

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and form a fundamental set on the interval . ; ... more

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and form a fundamental set on the interval . ; ... more

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, and does not form a fundamental set on the ... more

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Step 1: Step 2: Step 3: Step 4: more

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; The System of differential equations can be ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; In the System, . Find the characteristic ... more

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; To obtain the general solution using CAS, use ... more

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; To obtain the general solution using CAS, use ... more

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Phase portrait of system in problem 2 is:and half-... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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On comparing the equation with the general ... more

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; Write the system of differential equations into... more

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; The differential equation and can be written ... more

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; The differential equation and can be written ... more

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; The differential equation and can be written ... more

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; On comparing the equation with the general ... more

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; The differential equations , and can be ... more

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; The differential equations , and can be ... more

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; On comparing the equation with the general ... more

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  ; On comparing the equation with the general ... more

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  ; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; On comparing the equation with the general ... more

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; Apply the arithmetic operations to find the ... more

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; Using the eigen value functionality in CAS find... more

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Hi, there's no Problem 33 attached  more

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Step 1:Step 2:Step 3:Step 4: more

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Step 1:When eigenvalues are purely imaginary, the ... more

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; Write the differential equations , and in the ... more

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; Compare the equation with to find matrix .... more

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; Compare the equation with to find matrix .... more

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; Compare the equation with to find matrix .... more

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; Compare the equation with to find matrix .... more

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; Compare the equation with to find matrix .... more

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; Compare the equation with to find matrix .... more

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; First get the eigenvalues  and  corresponding  ... more

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; Rewrite the system into matrix for that is . ... more

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; Rewrite the system into matrix for that is . ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Given system Consider the corresponding ... more

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; Given system Consider the corresponding ... more

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; Given system Consider the corresponding ... more

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; Given system Consider the corresponding ... more

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; Given system Consider the corresponding ... more

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; Given system Consider the corresponding ... more

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; The System of differential equations can be ... more

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The electronegativity difference between N atoms ... more

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Ionic character can be defined by the ... more

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The lower the value of electronegativity ... more

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The ionic character of a compound depends on the ... more

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The bond character is calculated using the ... more

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The nature of the bonds is calculated on the basis... more

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Step 1:     Step 2:    Step 3:     Step 4... more

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; Determine the total valence electrons of OF2 by... more

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; Determine the total valence electrons of the ... more

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; Compute the total valence electrons that are ... more

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; Calculate the total valence electrons of the ... more

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; Compute the total valence electrons of the ... more

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; Determine the total valence electrons of the ... more

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; Determine the total valence electrons that are ... more

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; Count the total number of valence electrons. P ... more

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; Count the total number of valence electrons and... more

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; Count the total number of valence electrons. S ... more

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; Count the total number of valence electrons. ... more

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; Count the total number of valence electrons in ... more

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; The lewis structure represents the total number... more

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; The Lewis structure shows the number of valence... more

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; The Lewis structure represents the number of ... more

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; Given system is Compute and finding its ... more

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; Given system is Compute and finding its ... more

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; Given system is Compute and finding its ... more

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To find the eigenvectors of the matrix , solve . ... more

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To find the eigenvectors of the matrix , solve . ... more

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; Use the exponential matrix formula and expand ... more

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; The matrix can be written as . Same as the ... more

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; To find the integer, for , first find and ... more

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; Use computer algebra system (CAS) to obtain . ... more

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; Note that if then . Substitute the value for ... more

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and ; Apply the initial condition and to the ... more

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; Note that if is an eigen vector of then . ... more

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; The system has a complex eigen value of the ... more

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; The system of equations can be written in ... more

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; The system of equations can be written in ... more

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; The system of equations can be written in ... more

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; Evaluate to find the eigen values. ; Using ... more

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; Evaluate to find the eigen values. ; Using ... more

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Approach to solving the question: Detailed ... more

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; Evaluate to find the eigen values. ; Using ... more

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Step 1: Step 2: Step 3:Step 4: more

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; Substitute and in ; more

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