Differential Eq...

If $$y_1(x)$$ is a solution of the differential equation $$\frac{dy}{dx} + f(x) + y = 0$$, then a solution of differential equation $$\frac{dy}{dx} + f(x) + y = r (x)$$ is

Solution of differential equation $$\frac{dy}{dx} = sin(x+y) + cos(x+y)$$ is

Solution of differential equation $$\dfrac{dy}{dx} = \sin (x+y) + \cos(x+y)$$ is

The general solution of $$\dfrac {dy}{dx} = \dfrac {ax + h}{by + k}$$ represents a circle only when

$$Solution\quad of\quad the\quad equation:\quad (1-{ x }^{ 2 })dy\quad +\quad xydx=\quad x{ y }^{ 2 }dx$$

The solution of the differential equation $$x^{2} \dfrac{dy}{dx} = x^{2} + xy + y^{2}$$ is-

What is the solution of $$(1+2x)dy-(1-2y)dx=0$$?

Let $$f(x)$$ be a differential function and satisfy $$f(0) =2$$, and $$f'(x) = f(x)$$ . Find 

The solution of $$\left( {\cos ecx\log y} \right)dy + \left( {{x^2}y} \right)dx = 0$$ is

What is the solution of the differential equation $$xdy+ydx=0$$