# Math Help - Solving 1st order ODE

1. ## Solving 1st order ODE

Having some trouble, thanks. Im not sure what d_t(u) and :u(with the . above it) means. Would appreciate some help.

2. ## Re: Solving 1st order ODE

The symbol := means that the thing on the colon side is being defined as what's on the equals side. So the notation there is merely that

$\frac{du}{dt}$ is entirely equivalent to $d_{t}u,$ which is entirely equivalent to $\dot{u}.$

The actual differential equation is

$\dot{u}=g(t)u+h(t),\;u(0)=u_{0}.$

That, and the hint provided should get you started. What ideas do you have now?

3. ## Re: Solving 1st order ODE

Thanks, will give it a try!