Hi!
Let's say we have a system of DEs
$$
\begin{cases}
\frac{dx}{dt} = y + e^t\\
\frac{dy}{dt} = x - t^2\\
\end{cases}
$$
One would write it in matrix form and compute the eigenvectors and stuff like in this tutorial (can't post links due to low post count - it's from "Paul's online math...
Thanks for answering. Now I'm going to post the full solution; who knows, someone else might benefit from it.
Note that the procedure below might only work only if we're dealing with $sin$ or $cos$
The solution will be of this form (I do not know from where were you supposed to come up with...
Hi!
I need to find out how to solve this type of heat equations:
$$\large \frac{du}{dt} - \frac{d^2u}{dx^2} = \sin \pi x$$
$$\large u|_{t=0} = \sin 2\pi x $$
$$\large \large u|_{x=0} = u|_{x=1} = 0$$
I know what the solution to this but I can't solve it myself.
The problem is that all over...