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 byu(x) yieldinguy' + 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|

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