Consider the following system: $$x \frac{dx}{dt} + y \frac{dy}{dt} = 1$$ $$(y-2t) \frac{dx}{dt} - (x-2t) \frac{dy}{dt} = 0$$ Solve for $\frac{dx}{dt}$ and $\frac{dy}{dt}$.
The original problem is to find under which conditions this system has solution. However, is it possible to solve this system directly?