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

Options

A. ` e^(y) = (x^(3))/3 +C`
B. `e^(x) = (x^(3))/3 + e^(y) +C`
C. ` e^(y) = (x^(3))/3 + e^(x) +C `
D. None of these

Answer

c

Explanation

Here , `(dy)/(dx) = (e^(x))/(e^(y)) +(x^(2))/(e^(y))`
` rArr e^(y) dy = (x^(2)_e^(x)) dx`
This is variable separable form .
On integrating both sides, we get
` int e^(y) dy = int (x^(2) +e^(x)) dx rArr e^(y) = (x^(3))/3 + e^(x)+C`
which is the genereal solution of teh given differential equation , where C is an arbitrary constant .