Session 4.5 Using Laplace Transforms on a Differential Equation

> restart;

> with(inttrans):

> de:=D(D(y))(t)-y(t);

Define the differntial equation

> Fs:=laplace(de=sin(a*t), t, s);

Transform the equality with Laplace Transform

> ys:=solve(Fs,laplace(y(t),t,s));

Solve the function with the laplace transform as the variable.

> y(0):=1;D(y)(0):=0;

> yt:=invlaplace(ys,s,t);

Invert the solution

Thus, all that is required is a little simplification...

> yt:=unapply(yt,t);

> simplify(yt(0));

> simplify(D(yt)(0));

> a:=0.5;

> plot(yt(t),t=0...2);

>