Differential Eq...

Solution of $$\displaystyle \frac{dy}{dx}+\frac{y^{2}+y+1}{x^{2}+x+1}=0$$ is:

The order of differential equation $$\displaystyle \frac{d^{2}y}{dx^{2}}-\left ( \frac{dy}{dx} \right )^{2}=1$$ is:

A Function $$y=f(x)$$ stasfies $$\displaystyle  {f}''(x)=-\displaystyle \frac {1}{x^2}-\pi^2\sin(\pi x)$$; $$\displaystyle  {f}'(2)=\pi+ \displaystyle \frac{1}{2}$$ and $$f(1)=0$$. The value of $$f\left (\displaystyle  \frac{1}{2} \right )$$ is:

If $$f(x) = x+2;  g(x) = x^{2}-x-2$$, then $$\dfrac{g(1)+g(2)+g(3)}{f(-4)+f(-2)+f(2)}=$$

f:R r be defined by $$f(x)=3x-5,$$ the formula that defines the reverse $$f^n f^{-1}$$ is

If $$\displaystyle f\left ( 0 \right )={f}'\left ( 0 \right ) = 0$$ and $$\displaystyle {f}''\left ( x \right )=\tan ^{2}x$$ then $$\displaystyle f\left ( x \right )$$ is:

The differential equation $$\displaystyle \frac{dy}{dx}=\frac{\sqrt{1-y^{2}}}{y}$$determines a family of circles with:

If $$\frac{{dy}}{{dx}} = {e^{ - 2y}}$$ and $$y = 0$$ when $$x = 5$$, then value of x for $$y = 3$$ is

The general solution of differential equation is $$y=ae^{bx+c}$$ where $$a, b, c$$ are arbitrary constant. The order of differential equation is:

Find the solution of $$\displaystyle \frac{dy}{dx}=e^{x-y}+x^{2}e^{-y}$$.