Differential Equations › Section F · Series solutions › Topic F.3
Euler (Cauchy-Euler) equations
One family of variable-coefficient equations can be solved exactly, in closed form, even at a point where the series method breaks down. Euler equations show what solutions do near a singular point, and they are the model for the more general method that follows.
In this topic
- Powers matched to derivatives
- Trying a power of x
- Case 1: distinct real roots
- Worked example: an initial value problem
- Case 2: a repeated root
- Worked example: a double root
- Case 3: complex roots
- Why logarithms appear
- Negative x and other centres
- Common mistakes to avoid
- Key takeaways
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