This topic contains separate sections on how to find symbolic and numeric solutions since the techniques for solving those problems differ slightly. If you need to find derivatives or integrals of your solution, you should include equations for the derivatives and integrals in your system of ODEs. Most ODEs can be solved numerically even if they don't have a symbolic solution. Since they are integrated numerically, numeric solutions are approximations. Numeric solutions return a procedure that integrates your ODEs. However, if you are taking an introductory course in ODEs, it is most likely that you'll be interested in finding symbolic solutions.
Note that not every ODE or system of ODEs has a symbolic solution.
These solutions are exact and can be easily manipulated to find, for example, a value at a point, a derivative of the solution, or an integral of the solution. Symbolic solutions return equations that contains your independent variables. Unless noted otherwise, each example goes through the following steps:Īssigning the solutions to names (thus making them easier to plot and investigate).īefore you start looking at the examples on this page, you should consider what type of solution you need: symbolic or numeric. This topic introduces you to the commands and techniques used to solve ordinary differential equations (ODEs) in Maple.