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# Second order ODE !!??!£&@""&&"09&"?? Watch

1. The point lies on the curve such that

.

Find the possible equations of .

Any ideas?

Edit : I have put the correct question now. Also it's only first order actually.
2. (Original post by Ano123)
The point lies on the curve such that

.

Find the possible equations of .

Any ideas?
Why do you think an (elementary) solution exists?
3. (Original post by Zacken)
Why do you think an (elementary) solution exists?
This one does now.
4. (Original post by Ano123)
This one does now.
Now it makes sense.

Think of it as a quadratic in - this gets you or something along those lines.

It's a first order ODE, by the way - not a second order one.
5. (Original post by Ano123)
The point lies on the curve such that

.

Find the possible equations of .

Any ideas?

Edit : I have put the correct question now. Also it's only first order actually.
Consider differentiating both sides w.r.t. , and a lot of stuff cancels (but be careful not to lose any solutions when dividing through by a certain factor later). This will reduce the ODE to a trivial solution and a second order ODE that is "morally" a first order separable one.
6. I already have obtained the answers really. But it can always help to see how others do it.

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