Why is the number of essential arbitrary constants in the general solution of an ODE (ordinary differential equation) equal to the order of the ODE?
[Math] Number of arbitrary constants in the general solution of an ODE
ordinary differential equations
Best Answer
Hint:
How many constants do you find when you taking an indefinite integral?
Of course, one indefinite integral give us one constant in the result.
How many times we need to integrate an ODE of order two to get the final solution?
Obviously, we need two integrations. Every integration gives us one constant so we have two constants finally.
Do the same argument for higher order ODE. Note that, I assumed the ODE has a general solution and all needed conditions is provided in the question.