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# Differential Equation help. watch

1. Hey,

I need to show the following implication.

x is a solution to x'' + (a/t)x' + (b/t^2)x=0 iff y(u)=x(exp(u)) is a solution to y''+(a-1)y'+by=0

Where a.b are constants.

Now I have tried to use the chain rule on y(u)=x(exp(u)) then attempt to substitute and rearrange, but both the new variable u and the non constant coefficients of f(x'',x',x,t) are swaying me a bit.

Any help?

Thanks
2. (Original post by seanylpa)
...
Right, so you've got

Divide by and let etc.
3. How was that equation found?

I have managed to get to x''(exp(u))+a(x(exp(u))'+bx(exp( u))=0

Seany.
4. (Original post by seanylpa)
How was that equation found?

5. Ah of course Thank you

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