The general solution of the differential equation d x d y + x y =x^2 is

Step-by-step solution

Given differential equation is d x d y + x y =x^2 On dividing by x^2 , we get aligned & 1 x^2 d x d y + ( 1 y ) ( 1 x )=1 & let 1 x =t & - 1 x^2 d x d y = d t d y 1 x^2 d x d y =- d t d y & - d t d y + 1 y (t)=1 & d t d y + (- 1 y )(t)=-1 & I. F =e^ - 1 y d y =e^ - y = 1 y & aligned So, solution is aligned & t ( 1 y )= (-1) ( 1 y ) d y+c & t y =- y+c & t=-y y+c y & 1 x =c y-y y & aligned