Parameter variation method.

Mar 2020
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México
Can someone help me with this problem? y"-y=xe^× y(0)=1 y'(0)=0
 

topsquark

Math Team
May 2013
2,510
1,049
The Astral plane
Can someone help me with this problem? y"-y=xe^× y(0)=1 y'(0)=0
First solve \(\displaystyle y_h ^{ \prime \prime } - y_h = 0\) (The homogeneous solution.)

Then use variation of parameters for the particular solution. I'd start with \(\displaystyle y_p = Ax^2 e^x + B x e^x\)
(You could use \(\displaystyle y_p = A x^2 e^x + B x e^x + C e^x\) but the C term cancels out anyway.)

-Dan
 
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