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

If the differential equation $\begin{vmatrix} f(x) & f'(x) \\ f'(x) & f''(x) \end{vmatrix} = 0$ for all $x$ and $f(0) = 1, f'(0) = 2$, then...

The solution of the differential equation $x^2 \dfrac{dy}{dx} - xy = 1$ is...

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ ($0 < \theta < \pi$) is the angle between them, then the value of $\dfrac{|\bar{a} + \bar{b}|}{|\bar{a} - \bar{b}|}$ is equal to...