Maple ODE Examples

Here's a basic ODE:

> deq := diff(y(x),x) + y(x) = 0: deq;

Here's the basic form of the command for solving differential equations:

> soln := dsolve( deq, y(x) );

We can add initial conditions, to determine the "integration constant" _C1:

> subs(x=0, y(0)=y0, soln); solve(", _C1): subs(_C1=", soln);

This could be done in one step:

> dsolve( {diff(y(x),x) + y(x) = 0, y(0)=y0}, y(x) );

> dsolve({diff(y(x),x$2) + y(x) = x*cos(x), y(0) = y0, D(y)(0) = v0}, y(x));

> sys := diff(y(x),x)=z(x), diff(z(x),x)=y(x): sys;
inits := y(0)=0, z(0)=1: inits;
fcns := {y(x), z(x)}:

> dsolve({sys} union {inits}, fcns);

> dsolve({sys, y(0)=0, z(0)=1}, fcns, type=series);

This next example (the pendulum equation) is not solvable in terms of elementary functions. Maple obtains a "reduction to quadratures" for the inverse functions.

> dsolve({diff(y(x),x$2) + sin(y(x)) = 0}, y(x));

IU's involvement in the TeraGrid, and the presentation of this material is based upon work supported by the National Science Foundation under Grants No. 0833618, SCI451237, SCI535258, and SCI504075. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.