2nd order linear differential equation (homogeneous)

[jumbogala]

Homework Statement

Solve 354y`` −692y` + 235y =0

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

Homework Equations

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= C1e^0.94t + C2te^0.94t

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

y` = 0.94C1e^0.94t + 0.94C2te^0.94t + C2e^0.94t. Plugging in t = 0 we find that C2 = -2.61.

Therefore y = y= 7e^0.94t -2.61te^0.94t

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

 

[HallsofIvy]

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?

 

[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).

 

[jumbogala]

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