Q1.(a) Solve for the general solution using the method of variation of parameters:3y′′ + 6y′ + 3y = x^2*e^x(b) Find the particular solution subject to the initial condition y(0) = −1 and y′(0) = 1.(c) Use the substitution x = e^t, (x > 0) to transform the following Cauchy-Euler equation to a differential equation with constant coefficients, hence solve:x^2y''-xy'+4y=sinlogx+xcoslogx Q3.(a) Solve for the general solution using the method of variation of parameters:3y" + 6y'+ 3y = x²e*(b) Find the particular solution subject to the initial condition y(0) = –1 and y'(0) = 1.1(c) Use the substitution x = e', (x > 0) to transform the following Cauchy-Euler equation to adifferential equation with constant coefficients, hence solve:x’y" – xy' + 4y = sin log x + xcos log x

The given equation is 3y''+6y'+3y=x2ex a) We have to find the general solution of the equation using…

Answered: 1.(a) Solve for the general solution…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q1.(a) Solve for the general solution using the method of variation of parameters:

3y′′ + 6y′ + 3y = x^2*e^x

(b) Find the particular solution subject to the initial condition y(0) = −1 and y′(0) = 1.

(c) Use the substitution x = e^t, (x > 0) to transform the following Cauchy-Euler equation to a differential equation with constant coefficients, hence solve:

x^2y''-xy'+4y=sinlogx+xcoslogx

Q3.(a) Solve for the general solution using the method of variation of parameters:
3y" + 6y'+ 3y = x²e*
(b) Find the particular solution subject to the initial condition y(0) = –1 and y'(0) = 1.
1
(c) Use the substitution x = e', (x > 0) to transform the following Cauchy-Euler equation to a
differential equation with constant coefficients, hence solve:
x’y" – xy' + 4y = sin log x + xcos log x

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