# Thread: Need Help with second order DE with constant coefficients.

1. ## Need Help with second order DE with constant coefficients.

Hello - i need little help with this:
Find the particular solution:

blue - the problem
black - part of the solution

2. Have you taken the derivative of y?

You need to set y(0) = 2 and y'(0) = -2

3. 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

4. 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 $\displaystyle \displaystyle c_2$.

5. 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.

6. OK thanks i just wanted to be sure.. Thanks for the help