Question

求解图片中微分方程通解，需要详细过程，麻烦了，谢谢！！！！

Answer 1

let
u= y/x
du/dx = (xy' - y)/x^2

x.du/dx = y' - y/x
y' = u + x.du/dx
/
xy' - xsin(y/x) -y =0
y' - sin(y/x) -(y/x) =0
u + x.du/dx - sinu - u = 0
x.du/dx = sinu
∫cscu du =∫dx/x
ln|cscu- cotu | = ln|x| + C'
cscu- cotu = Cx
csc(y/x) - cot(y/x) = Cx