If y=y(x) is the solution of x d y d x =y+x e^ - ( y x ) , y(1)= e , then y ( e )=

Step-by-step solution

Which is a homogenous differential equation So let y x =v d y d x =v+x d v d x ...(ii) From eq ^ n (i) & (ii), we get aligned & v+x d v d x =v+e^ -v & x d v d x =e^ -v e^v d = d x x aligned Integrating both sides, we get aligned & y(1)= e=1 & (1)=e^1+c c=-e aligned Putting the value of c in equation (1), we get x=e^ y x -e