Linear first order differential equation

raul_l
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Homework Statement



\frac{dy}{dx} = \frac{x^2}{2} + \frac{xy}{2} + \frac{3y^2}{2} + \frac{3y}{2}

Homework Equations





The Attempt at a Solution



Don't really know were to begin. If anyone could tell me which method to use that would be great. I can't think of any way to solve this.
 
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That equation is NOT linear. I don't know if it will work but my first thought is to change coordinates to get rid of that "xy" term.
 

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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