Need help for finding an integrating factor that makes a

NepanitaNesg3a

NepanitaNesg3a

Answered question

2022-04-24

Need help for finding an integrating factor that makes a differential exact and solving it
ex(x+1)dx+(yeyxex)dy=0

Answer & Explanation

Ronnie Porter

Ronnie Porter

Beginner2022-04-25Added 12 answers

Step 1
It seems to me that you have made a mistake Nx=(yeyxex)x=xexex=ex(x+1), then you have NxMyM=1. And therefore its integrating factor will be μ(y)=ey. Multiplying the ODE by the integrating factor we have:
exy(x+1)dx+(yxexy)dy=0
Step 2
Thus having an exact ODE: Hence there is an F such that Fx=M and Fy=N. I think that from there you can continue on your own.

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