# 2nd order linear differential equation (homogeneous)

1. Oct 17, 2009

### jumbogala

1. The problem statement, all variables and given/known data
Solve 354y −692y + 235y =0

y(0) = 7
y(0) = 4

2. Relevant equations

3. The attempt at a solution
First I divided the equation by 354 to get y - 1.56y + 0.894y = 0.

Then I found the roots of this to be 0.94, repeated twice.

For repeated roots the solution looks like y= C1e0.94t + C2te0.94t

Using the initial conditions, solve. You find that C1 = 7.

y = 0.94C1e0.94t + 0.94C2te0.94t + C2e0.94t. Plugging in t = 0 we find that C2 = -2.61.

Therefore y = y= 7e0.94t -2.61te0.94t

But this isn't the correct answer. Where did I go wrong?

Last edited: Oct 17, 2009
2. Oct 17, 2009

### HallsofIvy

Staff Emeritus
You've rounded off incorrectly. -612/324 is 1.89 to two places, not 1.88. But I would be inclined to leave it as a fraction: 17/9. Are you allowed to do that?

3. Oct 17, 2009

### CompuChip

Apart from the fact that you rounded nearly every single number, why isn't the solution correct?
Because I got the same (up to rounding errors).

4. Oct 17, 2009

### jumbogala

Okay, I used fractions in my answer and that worked. Next time I'll be careful not to round carelessly... thanks!