Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Just want to quickly check that I have got this right: Am I right in thinking that the solution of $\dfrac{d^2y}{dx^2} = \sin(y)$ is $y(x) = 2 \arctan\left[\exp\left(\dfrac{x^2}{2}+ax+b\right)\right]$ where $a$, $b$ are constants of integration?

Thanks guys.

share|improve this question
It may be hard (impossible, even) to solve a differential equation, but it's easy to check whether a given function is a solution: you just pop it into the equation, and you see whether it works. Did you do this? –  Gerry Myerson Aug 14 '11 at 10:58
@Gerry: I tried differentiating the expression but I wasnt sure if it was just that I couldnt group the terms to give the correct form or if i was wrong... Now I see that it is the latter... –  scoobs Aug 14 '11 at 13:16

1 Answer 1

up vote 6 down vote accepted

Quick question, quick answer:

No, that doesn't look right. That's the pendulum equation, and its general solution contains a Jacobi elliptic function (not expressible in elementary functions).

share|improve this answer
Thanks, Hans. Where have I gone wrong? :( What I did was $csc(y) \frac{dy}{dx} = x+a$ then $log \left(tan\left(y/2 \right) \right) = (1/2) x^2 + ax + b$ ...? –  scoobs Aug 14 '11 at 10:28
@scoobs: The first integration is wrong; $\csc(y(x)) \, y''(x)$ isn't the derivative of $\csc(y(x)) \, y'(x)$. –  Hans Lundmark Aug 14 '11 at 10:52
Aha, thanks Hans. –  scoobs Aug 14 '11 at 13:14

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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