Solve differential equationdy/dx= x/(ye^(x+y^2))

Jaden Easton 2020-12-28 Answered

Solve differential equation dy/dx=x/(yex+y2)

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Expert Answer

Brighton
Answered 2020-12-29 Author has 103 answers

dy/dx=x/(yex+y2)
=>dy/dx=x/(yexey2)
=>ye(y2)dy=x/exdx
yey2dy=xexdx
ey2ydy=xexdx+c
where C is integrating constant
ey2ydy=xexdx+c
y2=t
2ydy=dt
ydy=(dt)/2
12etdt=xexdx+c(integrating by part)
12et=xex+exdx+c
1/2ey2=xex+(ex+c(t=y2))
1/2y2=ex[x+1]+c
1/2y2+en(x+1)=c
1/2y2=ex(x+1)+c
y2/2+ex(x+1)=C

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Jeffrey Jordon
Answered 2021-12-25 Author has 2495 answers

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