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February 11th, 2012, 02:36 AM   #1
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Differentiation

After differentation

dy/dx = x+y

will become, to find the exact solution

y = e^x - x - 1

I need to do the same to

dy/dx = y^3 (1-x^2)

Can anyone help?
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February 11th, 2012, 03:41 AM   #2
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Re: Differentiation

The second ODE is separable.




Finish it ...
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February 11th, 2012, 08:33 AM   #3
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Re: Differentiation

Would it be

-1/y=x-x^3/3
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February 11th, 2012, 10:26 AM   #4
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Re: Differentiation

For the first one you have



Put the equation like this



Multiply by









Notice we don't exclude the -1 as an arbitrary constant since it is part of the particular solution to the equation. is the solution to the homogeneous equation.
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February 12th, 2012, 04:25 AM   #5
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Re: Differentiation

Thanks for that but I need a bit more help with the second
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February 12th, 2012, 09:58 AM   #6
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Re: Differentiation

For the second you separate variables, putting











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February 12th, 2012, 01:15 PM   #7
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Or y = 0, which is the only real function that satisfies the equation for all real values of x.
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