> with(inttrans):

Problem #11 page 318

> laplace(diff(y(t),t,t)+4*y(t)=Heaviside(t-Pi)-Heaviside(t-3*Pi),t,s);

> subs({y(0)=0,D(y)(0)=0},%);

> solve(%,laplace(y(t),t,s));

> invlaplace(%,s,t);

To simplify this we tell Maple to collect terms that have and as factors.

> collect(%,[Heaviside(t-Pi),Heaviside(t-3*Pi)]);

To make this expression a function f(t) we use Maple command unapply.

> f:=unapply(%,t);

We should graph p(x) over the interval that includes and .

> plot(f,0..4*Pi);

Problem #19 page 331

> laplace(diff(y(t),t,t,t,t)+5*diff(y(t),t,t)+4*y(t)=g(t),t,s);

> subs({y(0)=1,D(y)(0)=0,(D@@2)(y)(0)=0,(D@@3)(y)(0)=0},%);

> solve(%,laplace(y(t),t,s));

> invlaplace((s^3+5*s)/(s^4+5*s^2+4),s,t);invlaplace(1/(s^4+5*s^2+4),s,t);

> -1/3*cos(2*t)+4/3*cos(t)+Int((-1/6*sin(2*u)+1/3*sin(u))*g(t-u),u=0..t);

Problem #9 page 324

> laplace(diff(y(t),t,t)+y(t)=Heaviside(t-Pi/2)+3*Dirac(t-3*Pi/2)-Heaviside(t-2*Pi),t,s);

> subs({y(0)=0,D(y)(0)=0},%);

> solve(%,laplace(y(t),t,s));

> invlaplace(%,s,t);

> collect(%,[Heaviside(t-1/2*Pi),Heaviside(t-3/2*Pi),Heaviside(t-2*Pi)]);