Differential Equation second degree help

kristo
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Homework Statement


\frac{dy}{dx}= y^2 + 1


Homework Equations





The Attempt at a Solution


I have no idea how to go about it. I've never solved a differential equation of second degree before.
 
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It may look scary, but it really isn't. Just divide both sides by (y2+1) then multiply both sides by dx. It's integrable from there.
 
Thanks a lot, I got it now. I keep forgetting the inverse trig derivatives.
 
No problem at all.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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