If (x^2+y^2 ) d y=x y ~d x , with y (x₀ )=e, y(1)=1 , then x₀ has the value

Step-by-step solution

aligned & . (x^2+y^2 ) d y=x y ~d x [Let y=v x ] & d y ~d x = x y x^2+y^2 & v+x d v ~d x = v 1+v & - 1+v^2 v^3 ~d v= d x x & 1 2 v^2 - v= x+ c & c y=e^ x^2 2 y^2 aligned [Let y=v x ] Putting x=1 and y=1 we get c=e^ - 1 2 y=e^ x^2-y^2 2 y^2 , now putting x=x₀ and y=e we get x₀= 3 e