Initially we solve the first order differential equation


where $a$, $b$ are constants. I derive the following with separation of variables


To find $D$ the initial condition is at $t=0$, $v=p$. How do I find $D$?

  • 1
    $\begingroup$ Plug in $t=0$ and $v=p$, it seems to give you $D$ directly in this case (no algebra required). Of course $D$ will depend on $p$ but that's OK. $\endgroup$ – Ian Nov 8 '18 at 16:10


Plug in $v=p$ and $t=0$ gives:

$$D = \sqrt{\frac{a}{b}}\arctan(p\sqrt{\frac{a}{b}})$$

Since $a,b,p$ are all constants $D$ is also a constant and you are done. The hardest part of course here was the solution itself.

| cite | improve this answer | |

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.