Are all linear second order differential equations in both real and complex spaces solvable by numer

racodelitusmn

racodelitusmn

Answered question

2022-07-03

Are all linear second order differential equations in both real and complex spaces solvable by numerical or analytical methods when we are given just the equation provided that a solution exists somewhere in both real and complex spaces.Solution could be of the form of an implicit equation, parametric equation, infinite series, elementary functions, special functions, etc. Will at least one of the methods work in general for linear second order partial differential ntial equations in general?

Answer & Explanation

poquetahr

poquetahr

Beginner2022-07-04Added 18 answers

The question is ambiguous because the meaning of "solvable" is not precise enough (in fact not defined). Do you mean :
Solvable on the form of an implicit equation ?
Solvable on the form of parametric equation ?
Solvable on the form of an infinite series ?
Solvable in terms of elementary functions ?
Solvable in terms of special functions ?
Etc.
Moreover an ODE can be not solvable yesterday and be solvable today in terms of special function. For example this is the case of y ( x ) + 1 x y ( x ) + y ( x ) = 0 which was not solvable in terms of special functions before the Bessel functions where defined studied and standardized.
Many special functions were standardized in order to make solvable some differential equations
Thus a today "non-solvable" ODE can become "solvable" tomorow not only because new methods of solving are likely to be invented but simply because new functions are likely to be defined and standardized.
The question is too wide for a definitive answer.If you just plug in the given x(t) into the equation, what do we get?

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?