> with(inttrans):

Uppgift nr 1.

> Ekv1:=diff(y(t),t$2)+2*4*diff(y(t),t)+(4^2-7^2)*y(t)=(exp(-11*t))*(4^2+7^2+6^2);

> dsolve({Ekv1,y(0)=4,D(y)(0)=7},y(t),method=laplace);

Uppgift nr 2.

> Ekv2:=diff(y(t),t$2)+4^2*y(t)=Heaviside(t-7)*sin(4*t);

> dsolve({Ekv2,y(0)=16+49,D(y)(0)=7^2+6^2},y(t),method=laplace);

Uppgift nr 3.

> Ekv3:=diff(y(t),t$2)+7^2*y(t)=7*Dirac(t-Pi);

> dsolve({Ekv3,y(0)=1,D(y)(0)=0},y(t),method=laplace);

> simplify(%);

> Värdet:=cos(7*5*Pi/4)-Heaviside(5*Pi/4-Pi)*sin(7*5*Pi/4);

> plot(cos(7*t)-Heaviside(t-Pi)*sin(7*t),t=0..10);

Uppgift nr 4 .

> transekv:=laplace(f(t),t,s)=4*laplace(cos(t),t,s)+7*laplace(int(exp(-6*tau)*f(t-tau),tau=0..t),t,s);

> laplace(f(t),t,s):=solve(transekv,laplace(f(t),t,s));

> f(t)=invlaplace(%,s,t);