Need Help with second order DE with constant coefficients.

**karagorge** · December 17th 2010, 07:10 AM

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

blue - the problem
black - part of the solution

**dwsmith** · December 17th 2010, 07:14 AM

Have you taken the derivative of y?

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

**snowtea** · December 17th 2010, 07:14 AM

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

**Prove It** · December 17th 2010, 07:14 AM

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 $\displaystyle c_2$ .

**Mondreus** · December 17th 2010, 07:15 AM

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.

**karagorge** · December 17th 2010, 07:25 AM

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

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