Given the second order non-homogeneous linear differential equation y+2y-3y 3 ex+ 4 cos x, (notation e^x= exp(x) = "e raised to the x power, cos x="cosine of x") find a particular solution yp of the non-homogeneous 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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For the PI how do I use the inverse operator when I write

3e^x/(1+3)(D-1)+4cosx/(D^2+2D-3)

3/4e^x/D-1+4cosx/-1+2D-3

3/4 x!/1! e^x + 4 cos x/-4+2D=3/4xe^x+2cosx/D-2

Using PI of 1/D-alphaQ = e^alpha x integrate e^-alpha Qdx. 
how do I proceed from there the steps for finding PI answers the full solution

 

Given the second order non-homogeneous linear differential equation
y+2y-3y=D3e'x+4 cos x,
(notation e*x=exp(x)-"e raised to the x power cos x= "cosine of x)
find a particular solution yp of the non-homogeneous equation.
Transcribed Image Text:Given the second order non-homogeneous linear differential equation y+2y-3y=D3e'x+4 cos x, (notation e*x=exp(x)-"e raised to the x power cos x= "cosine of x) find a particular solution yp of the non-homogeneous equation.
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