Differential Eq...

The solution of $$ \dfrac{dv}{dt} + \dfrac{k}{m}v = -g $$ is

The solution of the differential equation $$ x^{2}\dfrac{dy}{dx}\cos \dfrac{1}{x} - y\sin\dfrac{1}{x} = -1, $$ where $$ y \rightarrow -1 $$ as $$ x \rightarrow \infty $$ is

The solution of $$ ye^{-x/y}dx-(xe^{(-x/y)} + y^{3}) dy=0 $$ is

Solution of the differential equation $$ (y+x\sqrt{xy}(x+y))dx + (y\sqrt{xy}(x+y)-x)dy = 0 $$ is

Solution of differential equation $$ dy - \sin x \sin y dx = 0 $$ is

The solution of, $$ydx-xdy+(1+x^2)dx+x^2 \sin y dy=0$$,

The solution of differential equation $$ \dfrac{x+y\dfrac{dy}{dx}}{y-x\dfrac{dy}{dx}} = \dfrac{x\cos^{2}(x^{2} + y^{2})}{y^{3}} $$ is

The solution of $$\dfrac{dy}{dx}+x\sin 2y=x^{3}\cos^{2}y$$, is

The solution of the differential equation $$(e^{x^2}+e^{y^2})y\dfrac{dy}{dx}+e^{x^{2}}(xy^2-x)=0$$ is