Differential Eq...

if $$ y = y(x) $$ and $$ \dfrac{ 2 + sinx }{y + 1}(\dfrac{dy}{dx}) = -cosx, y(0) = 1, then y(\pi/2) $$ equals

Let $$f(x)$$ be a function such that $$f(0)=f'(0)=0, f''(x)=\sec^{4}x+4$$, then the function is

The solution of the equation $$ (x^{2}y + x^{2})dx + y^{2}(x-1)dy = 0 $$ is given by

Solution of $$ 2y sin x \frac {dv}{dx}= 2 sin x cos x -y^2 cos x, $$ for $$x = \frac { \pi}{2} , y = 1 $$ is 

If $$ \phi(x) =\int \left\{ \phi (x) \right\}^{-2} $$dx and $$ \phi ( 1) =0 $$ then $$ \phi (x) = $$

If $$ x\dfrac{dy}{dx} = y(\log y - \log x + 1) $$, then the solution of the equation is 

Solution of $$ \dfrac{dy}{dx} + 2xy = y $$ is 

The solution of differential equation $$ yy' = x\big(\dfrac{y^{2}}{x^{2}} + \dfrac{f (y^{2}/x^{2})}{f' (y^{2}/x^{2})}\big) $$ is

if integrating factor of $$ x(1-x^{2})dy + (2x^{2}y - y -ax^{3})dx=0 $$ is $$ e^{\int pdx} $$, then P is equal to 

The solution of differentiation equation $$(2y+xy^{3})dx+(x+x^{2}y^{2})dy=o $$ is