Is this differential equation a Bernoulli equation?

epkid08
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Homework Statement


Show that the differential equation is a Bernoulli equation by rewriting it in a different form:

y'=\frac{3x^2y - y^3}{2x^2}


I've tried numerous algebraic operations without any luck. Am I supposed to transform the equation algebraically to get it into Bernoulli form, or am I supposed to use a substitution, if so what substitution?
 
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I think just rearrange the equation algebraically would be ok. Try to write it in the standard form. What actually got you stuck?
 
Edit: I found my stupid mistake
 
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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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