Solve this equation pls y'+xy=e^x y(0)=1

Kye 2021-01-02 Answered
Solve this equation plsy+xy=ex
y(0)=1
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Expert Answer

SchepperJ
Answered 2021-01-03 Author has 96 answers

First, let us find the solution of the homogeneous equation
y+xy=0
We get,
y+xy=0
y=xy
dydx=xy
dyy=(x)dx
By integrating both sides, we get,
dyy=(x)dx
ln(y)x22+ln(C)
log(y)log(C)=x22
(yC)=x22
y=Cex22
So, the general solution of the given differential equation is given by
aex22+ex22exex22dx

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Jeffrey Jordon
Answered 2021-11-05 Author has 2064 answers

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