Originally Posted by

**Rapid_W** I suppose this is probably pretty easy for people in the know :p

Recently I've been using Wolfram Alpha, which is an amazing tool, I mainly like it for showing the steps in calculus, however it doesn't want to give the steps for differential equations :(

Anyway, the question is as follows...

$\displaystyle y'=5e^{4x}\sqrt{1-y^2}$

Now I know it's separable so I've put the square root bit under the y'

$\displaystyle \frac{y'}{\sqrt{1-y^2}}=5e^{4x}$

then I integrated both sides separately

$\displaystyle arcsin(y)=\frac{5}{4}e^{4x}+c$

leaving me with

$\displaystyle y=sin({\frac{5}{4}e^{4x}+c})$

However wolfram alpha is giving a rather more complicated answer of

$\displaystyle y=1+2sinh^2(\frac{1}{8}(4c+5ie^{4x}))$

So is WA wrong, or if it isn't, what steps have been taken to get to that answer?