Separable Differential Equation

mlowery
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Hello,
Yes, this is for a class - but it is simply a high school homework assignment.
I am solving for v. (This is only part of the homework problem, BTW).
http://mlowery.t35.com/AP_4_1a.jpg
My question is particularly concerned with the last two lines. On the final line, is the -64/5 necessary?

Thanks,
Mitchell
 
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of course. you can verify that otherwise, the original differential equation is not satisfied.
 
Thanks man. I guess I just wasn't thinking.

BTW, I am very impressed by these forums. It is a great resource and there are many interesting things to read.

Thanks,
Mitchell
 
It's great. There are so many knowledgeable people around. I sometimes feel like I'm learning more here than I do at school for 3000$ a year.
 
Haha, I guess I will find out next year.
 
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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