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Calculus / A First Course in Differential Equations with Modeling Applications 10 / Chapter 4.7 / Problem 51E

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

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Chapter 4, Problem 51E

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QUESTION:

Solve \(x^{3} y^{\prime \prime \prime}-x^{2} y^{\prime \prime}-2 x y^{\prime}+6 y=x^{2}\) by variation of parameters. Use a CAS as an aid in computing roots of the auxiliary equation and the determinants given in (15) of Section 4.6.

Text Transcription:

x^3 y^prime prime prime-x^2 y^prime prime-2 x y^prime+6 y=x^2

Questions & Answers

QUESTION:

Solve \(x^{3} y^{\prime \prime \prime}-x^{2} y^{\prime \prime}-2 x y^{\prime}+6 y=x^{2}\) by variation of parameters. Use a CAS as an aid in computing roots of the auxiliary equation and the determinants given in (15) of Section 4.6.

Text Transcription:

x^3 y^prime prime prime-x^2 y^prime prime-2 x y^prime+6 y=x^2

ANSWER:

Step 1 of 4

In this problem we have to solve the given differential equation by variation of parameters.

Given differential equation is ${x}^{3}{y}^{'''}-{x}^{2}{y}^{''}-2x{y}^{'}+6y={x}^{2}................(1)$

Auxiliary equation is $m(m-1)(m-2)-m(m-1)-2m+6=0$

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