Differential Eq...

The solution of the differential equation $${x}^{2}dy=-2xydx$$ is

If $$f:R \rightarrow R$$ be a continuous   function such that $$f(x)=\displaystyle \int^{x}_{1}2tf(t)dt$$, then which of the following does not hold(s) good?

Solution of the differential equation $$xdy-ydx=\sqrt {x^{2}+y^{2}}dx$$ is

Solution of the differential equation $$\dfrac{dy}{dx}+y\sec x=\tan x\left(\le x< \dfrac{\pi}{2}\right)$$ is 

The solution of the differential equation $$\cfrac{dy}{dx}=1+x+y+xy$$ is

A continuously differentiable function $$\phi(x)$$ in $$(0,\pi)$$ satisfying $$y'=1+{y}^{2},y(0)=0=y(\pi)$$ is

Solution of the differential equation $$(1+x^{2})dy+2xy dx=\cot x dx$$ is

The solution of the differential equation $$x^3 \dfrac{dy}{dx} + 4x^2 \tan y = e^x \sec y$$ satisfying $$y(1) = 0$$ is 

The solution of $$\cfrac{dy}{dx}=\cfrac{1+{y}^{2}}{\sec{x}}$$ is

The solution of $$ydx-xdy=0$$ is