desolve_system( [ equations ], [ variables ], [ , options ] )

The solution in SageMath of differential equations for dependent variables. The dependent variables must be declared as functions of the independent variable.

Equations in SageMath need to be defined with double equal (==) signs to avoid syntax errors.

Available options are:

ics=[initial_conditions]
ivar=independent_variable

Initial conditions are given for the independent variable, the dependent variable and all required derivatives of the dependent variable, in that order.

The independent variable must be specified if the equations contain more than one independent variable.

Solutions returned by Maxima can contain the three constants _C, _K1 and _K2, where the underscore distinguishes them from symbolic variables. They must be referenced in this form when substituting values or converting them to symbolic constants.

Examples:

y = function('y')(x)
z = function('z')(x)
desolve_system( [ diff(y,x,2) == 0, diff(z,x,2) == 0 ], [y,z] )

y = function('y')(x)
z = function('z')(x)
desolve_system( [ diff(y,x,2) + z == 0, diff(z,x,2) + y == 0 ], [y,z] )

y = function('y')(x)
z = function('z')(x)
desolve_system( [ diff(y,x,2) + z == 0, diff(z,x,2) + y == 0 ],
                    [y,z,diff(y,x),diff(z,x)], ics=[0,1,2,3,4] ) )

Related operations:   desolve_system_rk4

Operation category: solution operations sagemath-docs