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Friday, October 29, 2010

Recipe for solving linear first order ODE

As I blogged before I am going to make more notes, summaries and stuff and store everything in a plex in a Personal Brain database. The following note basically summarizes 18.03 lecture 3.

$$a(x) \cdot y' + b(x) \cdot y = c(x)$$
$$y' + p(x) \cdot y = q(x)$$
$$e^{\int{p(x) \ dx}} \cdot y' + p(x) e^{\int{p(x) \ dx}} \cdot y = e^{\int{p(x) \ dx}} q(x) $$
$$( e^{\int{p(x) \ dx}} \cdot y )'= e^{\int{p(x) \ dx}} q(x) $$
$$e^{\int{p(x) \ dx}} \cdot y= \int{e^{\int{p(x) \ dx}} q(x) \ dx} $$
$$y= \frac{\int{e^{\int{p(x) \ dx}} q(x) \ dx}}{e^{\int{p(x) \ dx}}} + \frac{C}{e^{\int{p(x) \ dx}}}$$

( Would need some explanations but as a personal note it is clear to me. )

1 comment:

  1. Really neat Nilo I need to learn about LATEX for my own blog any suggestions as to how I can the required information ?


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