|
dsolve/formal_solution - find formal solutions to a homogeneous linear ODE with polynomial coefficients
|
|
Calling Sequence
|
|
dsolve(ODE, y(x), 'formal_solution', 'coeffs'=coeff_type, 'point'=x0)
dsolve(ODE, y(x), 'type=formal_solution', 'coeffs'=coeff_type, 'point'=x0)
|
|
|
Parameters
|
|
|
ODE
|
-
|
homogeneous linear ordinary differential equation with polynomial coefficients
|
|
y(x)
|
-
|
dependent variable (the indeterminate function)
|
|
'type=formal_solution'
|
-
|
(optional) request for formal solutions
|
|
'coeffs'=coeff_type
|
-
|
(optional) coeff_type is one of 'mhypergeom', 'dAlembertian'
|
|
'point'=x0
|
-
|
algebraic number, rational in parameters, or infinity
|
|
|
|
|
|
Description
|
|
|
•
|
When the input ODE is a homogeneous linear ode with polynomial coefficients, and the optional arguments 'formal_solution' (or 'type=formal_solution') and 'coeffs'=coeff_type are given, the dsolve command returns a set of formal solutions with the specified coefficients at the given point (the default is at the origin). For more information, see Slode[mhypergeom_formal_sol] and Slode[dAlembertian_formal_sol].
|
|
|
|
Examples
|
|
Find the formal solution set with m-hypergeometric series coefficients.
|
>
|
|
|
| (1) |
|
>
|
|
|
| (2) |
Find the formal solution set with d'Alembertian series coefficient.
|
>
|
|
|
| (3) |
|
>
|
|
|
| (4) |
|
>
|
|
|
| (5) |
|
>
|
|
|
| (6) |
|
|
Download Help Document
Was this information helpful?
