Hello - i need little help with this:

Find the particular solution:

http://img585.imageshack.us/img585/8097/task.png

blue - the problem

black - part of the solution

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- Dec 17th 2010, 07:10 AMkaragorgeNeed Help with second order DE with constant coefficients.
Hello - i need little help with this:

Find the particular solution:

http://img585.imageshack.us/img585/8097/task.png

blue - the problem

black - part of the solution - Dec 17th 2010, 07:14 AMdwsmith
Have you taken the derivative of y?

You need to set y(0) = 2 and y'(0) = -2 - Dec 17th 2010, 07:14 AMsnowtea
Use the conditions y(0) = 2, and y'(0) = -2

y(0) = (c1) + (c2) = 2

y'(0) = -3(c1) + (c2)/3 = -2

Solve for c1 and c2

And you have the particular solution for y - Dec 17th 2010, 07:14 AMProve It
This is a homogeneous DE, you don't need to find a particular solution.

Just substitute your boundary conditions, noting that $\displaystyle \displaystyle y' = -3c_1e^{-3x} + \frac{c_2}{3}e^{\frac{x}{3}}$, to evaluate $\displaystyle \displaystyle c_1$ and $\displaystyle \displaystyle c_2$. - Dec 17th 2010, 07:15 AMMondreus
So what's the problem? You've already done the hard part. Insert the conditions $\displaystyle y(0)=2$ and $\displaystyle y'(0)=-2$ into your solution (and the derivative of it) and you'll end up with a system of linear equations that is easy to solve.

- Dec 17th 2010, 07:25 AMkaragorge
OK thanks i just wanted to be sure.. Thanks for the help :)