need help w/separation of variables

[mmolini]

y'=xe^(y-x^2)
Do I just take the ln of both sides
ln dy=lnxe^(y-x^2) dx
ln dy=ln(x)-x+y

 

[JohnZ]

y'=xe^(y-x^2)
Do I just take the ln of both sides
ln dy=lnxe^(y-x^2) dx
ln dy=ln(x)-x+y

you can not separate variables this way.
y'=x*e^(y-x^2)=x*e^y*e^(-x^2)
y'/e^y=x*e^(-x^2)

 

[chandra21]

Nxt

you can not separate variables this way.
y'=x*e^(y-x^2)=x*e^y*e^(-x^2)
y'/e^y=x*e^(-x^2), integrating
int dy/e^y=int x*e^(-x^2)dx+c
-e^y= e^(-x^2)+c

 

[Deleted member 4993]

The above solution is not correct. Instead it should be,

you can not separate variables this way.
y'=x*e^(y-x^2)=x*e^y*e^(-x^2)
y'/e^y=x*e^(-x^2)

\(\displaystyle \displaystyle{\int e^{-y}dy \ = \ -\frac{1}{2}\int -2*x*e^{-x^2}dx }\)

\(\displaystyle \displaystyle{-e^{-y} \ = \ -\frac{1}{2}e^{-x^2} + C }\)