Question

Solve the differential equation

Answer 1

Let the differential equation is y e x y dx=( x e x y + y 2 )dy,( y≠0 ), y=−1 when x=0

Simplify above equation.

y e x y dx=( x e x y + y 2 )dy y e x y dx dy =( x e x y + y 2 ) e x y { y dx dy −x }= y 2 e x y ×[ { y dx dy −x } y 2 ]=1 (1)

Let e x y =z and differentiating with respect to y.

d dy ( e x y )= dz dy e x y d dy { x y }= dz dy e x y [ { y dx dy −x } y 2 ]= dz dy (2)

On comparing equation (1) and (2), we get

dz dy =1 dz=dy

By integrating both side of the above equation, we get

z=y+C e x y =y+C

Thus, the above equation is required solution for differential equation.