## Ordinary Differential Equations

## 1st order ODE

\frac{dy}{dt} + p(t) y = q(t)

The general solution is

y = \frac{\int \mu(t) q(t) dt + C}{\mu(t)}

where the integration factor μ is

\mu(t) = e^{\int p(t) dt}

\frac{dy}{dt} + p(t) y = q(t)

The general solution is

y = \frac{\int \mu(t) q(t) dt + C}{\mu(t)}

where the integration factor μ is

\mu(t) = e^{\int p(t) dt}