Differential Equations Tutorials

driven4rhythm
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I was wondering if anyone has any good resources for differential equations? I've been using Paul's Notes all semester but they don't cover the last chapter of my book. The chapter is Nonlinear Differential Equations and Stability. The topics are The Phase Plane: Linear Systems, Autonomous Systems and Stability, Locally Linear Systems, Competing Species, and Predator-Prey Equations. Any help would be greatly appreciated.
 
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Please study differential equation and boundary value problems by zill.
Aamir507
 

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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