# Need Help with second order DE with constant coefficients.

• Dec 17th 2010, 07:10 AM
karagorge
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
• Dec 17th 2010, 07:14 AM
dwsmith
Have you taken the derivative of y?

You need to set y(0) = 2 and y'(0) = -2
• Dec 17th 2010, 07:14 AM
snowtea
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 AM
Prove It
This is a homogeneous DE, you don't need to find a particular solution.

Just substitute your boundary conditions, noting that $\displaystyle y' = -3c_1e^{-3x} + \frac{c_2}{3}e^{\frac{x}{3}}$, to evaluate $\displaystyle c_1$ and $\displaystyle c_2$.
• Dec 17th 2010, 07:15 AM
Mondreus
So what's the problem? You've already done the hard part. Insert the conditions $y(0)=2$ and $y'(0)=-2$ 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 AM
karagorge
OK thanks i just wanted to be sure.. Thanks for the help :)