`(dy)/(dx)=(y)/(x)+x sin((y)/(x))`

The general solution of the DE (dy)/(dx) = (y)/(x) + sin ""(y)/(x) is

(dy) / (dx) = (y) / (x) + sin ((y) / (x))

Solve: (dy)/(dx)+(y)/(x)=cos x+(sin x)/(x)

(dy)/(dx)=sin(x-y)

(dy)/(dx)=e^(-y)sin x+e^((x-y))

The degree and order of differential equatiion (x+y(dy)/(dx))^((1)/(2))=(x sin x((dy)/(dx))^(2)+y)/(((dy)/(dx))^(3)) is :

(dy)/(dx)=e^(-y)*sin x+e^((x-y))

Solution of the differential equation (x+y(dy)/(dx))/(y-x(dy)/(dx))=(x sin^(2)(x^(2)+y^(2)))/(y^(3))

(dy/dx)+(y/x)=sin x^(2)

(dy)/(dx)+y=sin x