Non linear 2nd order differential equation

chumlee
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please provide step by step method to solve this 2nd order non linear differential equation:
attached with this thread. take FUCOS(Ѡt) and FUsin(Ѡt) as zero.
 

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Sorry, Chum, it's against the rules of PF to solve things for you. You've got to show some of your own work in order to get help.

Is this for HW?
 
see new attached pdf file
 
chumlee said:
please provide step by step method to solve this 2nd order non linear differential equation:
attached with this thread. take FUCOS(Ѡt) and FUsin(Ѡt) as zero.

chumlee said:
see new attached pdf file

Thread moved to HH/Calculus.

It looks like the PDF helps to define the problem, but you still need to show some effort on the math questions that you are asking. What approach do you think you should use?
 
Chumlee, here are the instructions you are missing and the template you need to fill out.

Use the template provided

• You must show your attempt at solving the problem
• Write the text of the problem here, not in an attachment or an image.

Template

Homework Statement




Homework Equations




The Attempt at a Solution

 

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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