3) x³y(3)-3x²y" + 6xy' – 6y = 12x*sin2 () for differential equation a) Find the homogeneous solution. b) Find the special solution of the non-homogeneous equation using the method of change of parameters. c) Find the general solution of the inhomogeneous equation.

3) x³y(3)-3x²y" + 6xy' – 6y = 12x*sin2 () for differential equation a) Find the homogeneous solution. b) Find the special solution of the non-homogeneous equation using the method of change of parameters. c) Find the general solution of the inhomogeneous equation.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

3) x³y(3)-3x²y" + 6xy' – 6y = 12x*sin2 ) for differential equation
a) Find the homogeneous solution.
b) Find the special solution of the non-homogeneous equation using the method of change of
parameters.
c) Find the general solution of the inhomogeneous equation.

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