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- Basic structure of ODESolve
- ===========================
- One general rule is never to convert a linear ODE into a nonlinear
- ONE!
- Classification strategy:
- 1. LINEAR (return either basis or linear combination)
- (a) first order - integrating factor - module odelin
- (b) higher order:-
- (i) n-th order (trivial) - special case of (ii)
- (ii) constant coeffs - module odelin
- (iii) polynomial coeffs:-
- factorizable (algebraically) - handled by making monic
- Euler & shifted Euler - module odelin
- dependent variable missing - module odelin
- exact - module odelin
- variation of parameters (for P.I.) - module odelin
- special functions (e.g. Bessel) - module odelin
- polynomial solutions - ???
- adjoint - ???
- operational calculus - ???
- order reduction - ???
- factorizable (operator) - ???
- Lie symmetry - ???
- 2. NONLINEAR
- main module odenonln(?)
- (a) first order:-
- Prelle-Singer - TO DO
- Bernoulli - done
- Clairaut - done
- contact - ???
- exact - done
- homogeneous - done
- Lagrange - done
- Riccati - done
- Solvable for x/y - done
- Separable - done
- (b) higher order:-
- dependent variable missing - done
- factorizable (algebraically) - done
- factorizable (operator) - trivial version done
- autonomous - done
- differentiation - done
- equidimensional - done
- exact - done
- scale invariant - done
- contact - ???
- Lie symmetry - ???
- (c) any order
- interchange variables - done
- (undetermined coefficients ?) - ???
- A potential problem with this strategy is that one cannot easily pass
- back an unsolved ode through the interchange chain. Using more
- symbolic mode might solve this. For the time being, unsolved odes are
- not passed back at all, but does this lose partial solutions? THIS
- NEEDS CHECKING MORE CAREFULLY!
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