The solution of $\frac{dy}{dx} = \frac{1}{x}$ is

The function $f(x)$ satisfies the differential equation $f^2(x) + 4f'(x)f(x) + [f'(x)]^2 = 0$. Find the general solution for $f(x)$,where $c$ is an arbitrary constant.

Show that the general solution of the differential equation $\frac{dy}{dx} + \frac{y^{2}+y+1}{x^{2}+x+1} = 0$ is given by $(x+y+1) = A(1-x-y-2xy)$,where $A$ is a parameter.

The general solution of the differential equation $\cos(x+y) dy = dx$ is

The differential equation $\cos (x+y) dy = dx$ has the general solution given by

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is