The general solution of `(dy)/(dx) = 2x e^(x^(2)-y)` is

Options

A. `e^(x^(2)-y)= C`
B. ` e^(-y) + e^(x^(2)) = C`
C. ` e^(y) = e^(x^(2)) + C`
D. `e^(x^(2)+y)=C`

Answer

c

Explanation

Given that , `(dy)/(dx) =2x *e^(x^(2)-y)`
` rArr int e^(y) dy = int 2xe^(x^(2))dx [ "put" x^(2)= =t , 2xdx= dt ]`
` rArr int e^(y) dy = int e^(t) dt`
` rArr e^(y) = e^(t) +C`
` rArr e^(y) = e^(x^(2)) +C " " [ :' t = x^(2)]`