# Math Help - solution of ODE

1. ## solution of ODE

Can someone answer this question? stuck!
Find the solution u(t) of the ODE
$
3 \frac {d^2 x} {dt^2} - 2 \frac {du} {dt} - u = 0
$

which satisfies u = 1, $\frac {du} {dt}$ at t=0

2. Originally Posted by mongmong
Can someone answer this question? stuck!
Find the solution u(t) of the ODE
$
3 \frac {d^2 x} {dt^2} - 2 \frac {du} {dt} - u = 0
$

which satisfies u = 1, $\frac {du} {dt}$ at t=0
Is it meant to be $3 \frac {d^2 {\color{red}u}} {dt^2} - 2 \frac {du} {dt} - u = 0$ ?

This is a second order homogenous linear differential with constant coefficients and there are a ton of websites that explain how to solve it.

3. Yes