The solution of d x ~d y + x y =x^2 is

Step-by-step solution

d x ~d y + x y =x^2 1 x^2 d x ~d y + 1 x y =1.. (i) Let 1 x = t Differentiating w.r.t. y , we get array ll & -1 x^2 d x ~d y = dt d y 1 x^2 d x ~d y = - dt d y & (i) - dt d y + t y =1 & dt d y - t y =-1 & I.F. = e ^ -1 y ~d = e ^ ( 1 y ) = 1 y array The solution of the given equation is aligned t ( I . F ) & = (-1)( I.F. ) d y+ c t ( 1 y ) & = -1 y ~d y+ c t y & =- y+ c 1 x y & =- y+ c 1 x & = c y-y y aligned