General solution of a differential equation (separable)

hpayandah
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Homework Statement


Find the general solution of the differential equation y'=4t-ty^2

Homework Equations


y'=4t-ty^2


The Attempt at a Solution


I 'think' this question is pretty straight forward but I'm still not sure if I did it right or not. I have two question. One till the last step that I have done, have I done it correctly 2. How do I proceed from there? The attempt is attached.
 

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What you've written is correct. Normally, you should know on what subset of R you're looking for y. If not, then keep the modulus there and don't explicitate.
 
dextercioby said:
What you've written is correct. Normally, you should know on what subset of R you're looking for y. If not, then keep the modulus there and don't explicitate.

The proff didn't give any range for y. So by don't explicitate you mean I should keep it the way it is?
 

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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