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1 Pattern matching

1.1 Detect reduced Riccati ode \(y'=a x^n + b y^2\)
1.2 Detect general Riccati ode \(y'=f_0(x) + f_1(x) y(x)+ f_2(x) y^2\)
1.3 Detect ode of form \(y'=(a + b x + c y(x))^n\)
1.4 Detect first order linear ode of form \(A(t) y'(t)+ B(t) y(t)=f(t)\)
1.5 Detect second order linear ode of form \(A(t) y''(t)+ B(t) y'(t) + C(t) y(t)=f(t)\)
1.6 pattern example 1
1.7 pattern example 2
1.8 pattern example 3
1.9 pattern example 4
1.10 pattern example 5
1.11 pattern example 6
1.12 pattern example 7
1.13 pattern example 8
1.14 pattern example 9
1.15 pattern example 10
1.16 pattern example 11
1.17 pattern example 12
1.18 pattern example 13
1.19 pattern example 14
1.20 pattern example 15
1.21 pattern example 16
1.22 pattern example 17
1.23 pattern example 18
1.24 pattern example 19

This section shows some examples using Maple to detect some patterns. In all of these the main maple function used is patmatch. Some example also show the Mathematica command to compare results with.

Many of these can be done in Maple without using patmatch command, and even using shorter code. But these examples are meant to show how to use patmatch.

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