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As the title says, I am asked to specify a differential equation with the solution $y = 3 \sin(4x + v)$; boundary conditions are not required.

I have a question from my book and don't know how to deal with it! How do I do it? Thank you in advance...

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If you want a second order differential equation then you can construct like y''+C\,y=0 . Can you find what the constant $C$ is going to be for your case?

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    @Mario: for a second order equation you need two boundary conditions. To make $y(0)=3$ in your original equation you need $3sin v=3$.2011-05-25
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I'll do a related question. Suppose I were asked to give a differential equation with answer $y = e^{2x}$. Then I might note that the second derivative of y is $4e^{2x}$ and the first derivative is $2e^{2x}$. But then y is just a solution to y'' + 2y' = 8e^{2x}.

Does that make sense?

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    @Mixedmath, many thanks for your help! I really learned alot ;-)2011-05-25