Uncovering the Bernoulli Equation: Solving y'+P(x)y=Q(x)y^n

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Homework Statement


I think this is a bernoulli equation in disguise
(y^7-6x)y'+y=0

Homework Equations


I'm having trouble putting it in the form of y'+P(x)y=Q(x)y^n


The Attempt at a Solution


I've tried to divide out (y^7-6x) as well as some other alebraic manipulation but i keep getting stuck. Any advice?
 
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anyone?
 
physicsnewb7 said:
anyone?

Try writing it in terms of x = x(y) and using:

<br /> y&#039; = \frac{1}{x&#039;}<br />
 

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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