particular solution of the given differential equation

Question

i need help solving this problem 

 

Find the particular solution of the given differential equation
dy/dx=−6xe^(y−x^2) ;y=12 when x=1.

Answer 1

Here's how to separate variables.

dy/dx = -6e^{-x^2} / e^-y

Now cross-multiply and the variables are separated. You just have to know how to antidifferentiate e^{-x^2}