Particular maximal solution of the inhomogeneous equation $y^{'} = |t|y + t$ on $\mathcal I = \mathbb R$.

I've already solved this system in the homogeneous case $b(t)=0$, where I've found the solution (maximal) to be $t \mapsto \eta e^{\int_{t_0}^t |s| ds}$.

However, not I'm looking for a particular maximal solution of the inhomogeneous equation.

Maple gave me the following output:

enter image description here

However, this is by no means useful ? There got to be a way of finding a "nice looking" and "easy to interpret" solution ?

  • $\begingroup$ Sorry, I did a typo. I've now corrected everything. $\endgroup$ – Shuzheng Feb 17 '15 at 8:30

If I'm not wrong, the solution given by Maple is "nice and easy to interpret", it just defined by parts :

$\left\lbrace \begin{array} f(x) = e^{\frac{x^2}{2}}+Ce^{-\frac{x^2}{2}} & if & x \leq 0 \\ f(x) = -e^{-\frac{x^2}{2}}+Ce^{\frac{x^2}{2}} & if & x > 0 \end{array} \right.$

  • $\begingroup$ Thank you, but I did a typo. It is corrected. $\endgroup$ – Shuzheng Feb 17 '15 at 8:31
  • $\begingroup$ Oh, right, didn't see the typo $\endgroup$ – Tryss Feb 17 '15 at 8:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.