Solving a Homogeneous ODE:

> homo:=diff(u(t),t,t)+u(t)=0;

> dsolve(homo,u(t));

Solving an Inhomogeneous ODE:

> inhomo:=diff(u(t),t,t)+u(t)=1-exp(-t);

> dsolve(inhomo,u(t));

> simplify(%);

Using Undetermined Coefficients

> undet:=subs(u(t)=A+B*exp(-t),inhomo);

> undet:=eval(undet);

We can see that A=1 and B=-1/2, which agrees with the above result.

• Download the Maple worksheet.