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Second order ODE homogeneous, quick question watch

1. Hi,

I think I may have forgotten some basic things so I think it's just a quick one.

If you have a first order ODE I know you would do a integrating factor for something similar, but for this second order equation I have forgotten the trick or how to find the integrating factor:

Many thanks for your help !
2. (Original post by xfootiecrazeesarax)
Hi,

I think I may have forgotten some basic things so I think it's just a quick one.

If you have a first order ODE I know you would do a integrating factor for something similar, but for this second order equation I have forgotten the trick or how to find the integrating factor:

Many thanks for your help !
I believe the substitution will help to simplify this down for you to a fairly simple ODE

Edit: Also I think the substitution is another one you can use.
3. (Original post by xfootiecrazeesarax)
Hi,

I think I may have forgotten some basic things so I think it's just a quick one.

If you have a first order ODE I know you would do a integrating factor for something similar, but for this second order equation I have forgotten the trick or how to find the integrating factor:

There are various options here: If you have a DE of the form

, you can solve it by guessing at solutions of the form in a very similar way to how we solve . (Note that you can't "just" plug \alpha into the polynomial with the same coefficients, because the kth derivative of is not , but otherwise it is very similar).

[This is very similar to the r = e^u suggestion from the previous poster].

If you have a 2nd order DE with no constant term, you can reduce it to a first order DE by the substitution y = dc/dr. Solve the first order DE tind y, then add an arbit constant to find c.

Finally, you could recognize that . (This last is quite a "specific" trick, but derivatives of this form come up enough that you should be able to recognize them and variants without too much trouble).

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