## MIT 1803 lecture 3

Watched MIT Maths lecture 3 on solving first order linear ODEs (steady state and transient solutions) with Arthur Mattuck.   The lecture was good, and showed me what I hadn’t seen before, the general method of solving a first order ODE.  The process is as follows

1. Refactor given equation into $y' + p(x)y = q(x)$ which is known as standard linear form
2. Find the integrating factor $u(x)$ such that the left hand side can be expressed as $(uy)' = q(x)$ which implies that $u(x) = e^{\int p(x) dx}$
3. Multiply the original equation (1) through by$u(x)$ yielding$uy' + upy = uq$ which can also be written as $(uy)' = uq$
4. Integrate both sides and divide by $u$ to yield a solution for $y$ thus $y = (1/u) \int (uq) dx$

He worked two examples which I tried to work first.  I’ve relearned $\int du/u = \ln|u|$