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# Differential equations watch

1. Hi

haven't done these for a while so I might be missing something simple but can anyone give me any pointers on...

dy/dx = (c^2 - (k^2)(y^2))^0.5

thanks
2. This is a separable differential equation; that is, it's in the form (where are functions of , respectively). In general, the method is to rearrange the equation to get . Integrating both sides w.r.t. x then gives .

If you can't work out what f(x) and g(x) are

No really, try to find them first

You can use and .
3. (Original post by nuodai)
This is a separable differential equation; that is, it's in the form (where are functions of , respectively). In general, the method is to rearrange the equation to get . Integrating both sides w.r.t. x then gives .

If you can't work out what f(x) and g(x) are

No really, try to find them first

You can use and .

Thanks
I did actually separate them like that! But I thought it was wrong because I didn't know how to integrate 1/RHS wrt y...
4. (Original post by bonbon)
Thanks
I did actually separate them like that! But I thought it was wrong because I didn't know how to integrate 1/RHS wrt y...
Ah yes, I should have mentioned: the substitution might help. Or if you're a formula book addict, look for the integral in the form .
5. (Original post by nuodai)
Ah yes, I should have mentioned: the substitution might help. Or if you're a formula book addict, look for the integral in the form .

ah ok thanks. should get it from here thanks

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