# Find $N$ independent solutions through Laplace Transform

The Laplace Transform method gives us one solution of an Ordinary Differential Equation. How can we use the same procedure to get $N$ independent solutions, being $N$ the order of the ODE? Where can I find a proof of this procedure?

Thanks a lot!

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What made you to think that you could use L.T. for such that OE? –  Babak S. Apr 6 '13 at 13:03
Try to solve the simple ode $y''- y=0$ using L.T technique and see how many solutions you get! –  Mhenni Benghorbal Apr 6 '13 at 13:24
@BabakS. Because it's done in fractional differential equations which are a generalization of ODE's. –  Ambesh Apr 6 '13 at 13:30
@MhenniBenghorbal My problem is not a particular case. I'm searching for a general theorem+proof. –  Ambesh Apr 6 '13 at 13:33
I understand this. But, who said that L.T technique does not give all the $n$ linearly independent solutions? –  Mhenni Benghorbal Apr 6 '13 at 13:43