All students taking a degree in a quantitative science sooner or later will have to solve a differential equation of some kind. There are no general rules for solving differential equations, but in the last three centuries mathematicians have done their best to classify some of them and find methods to derive analytic solutions for a wide sample of cases.

In this page I have collected a few personal notes to be (hopefully) used in future teaching. Only those cases I have dealt with are listed. Analytic solutions have been found for many more equations and interested students or researchers should look up specialised texts.

- Exact equations (Postscript) (PDF)
- First order linear equations (Postscript) (PDF)
- First order homogeneous equations (Postscript) (PDF)
- Bernoulli's equation (PDF)
- Reduction of order for linear second order equations (Postscript) (PDF)
- Homogeneous equations with constant coefficients (Postscript) (PDF)
- Variation of parameters for non-homogeneous equations (Postscript) (PDF)
- General properties for second order linear differential equations (Postscript) (PDF)
- Linear systems of first order differential equations (Postscript) (PDF)

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