ENGI 2422 Engineering Mathematics 2
Maple 6 Version for
part of Problem Set 10

> with(inttrans):
ENGR 2422 Engineering Mathematics 2 Winter 2007 Problem Set 10
Question 2(a)
> laplace(t^4*exp(-2*t),t,s);

Question 2(b)
> laplace(t+(exp(1-t)-t)*Heaviside(t-1),t,s);

> simplify(%);

Question 2(c)
> laplace(4*(sin(3*t))^2,t,s);

Question 2(d)
> laplace(exp(-t)*Dirac(t-2),t,s);

Question 2(e)
> laplace(t*exp(-2*t)*cos(3*t),t,s);

> simplify(%);

Question 3(a)
> invlaplace((s+4)/(s^2+16),s,t);

Question 3(b)
> invlaplace(((s+1)^2-16)/((s+1)^2+16)^2,s,t);

Question 3(c)
> invlaplace((6*s^3+28*s^2+21*s+26)/(s^4+4*s^3+13*s^2),s,t);

Question 3(d)
> invlaplace((1+(s-1)*exp(-s))/s,s,t);

Question 4(a)
> ode1 := {diff(y(t),t,t) - 3*diff(y(t),t) - 10*y(t) = 1}:
> ic := {y(0)=1, D(y)(0)=1}:
> dsolve(ode1 union ic, {y(t)});

Question 4(b)
> ode1 := {diff(y(t),t,t,t) + 3*diff(y(t),t,t) + 3*diff(y(t),t) + y(t) = exp(-t)}:
> ic := {y(0)=0, D(y)(0)=0, (D@@2)(y)(0)=0}:
> dsolve(ode1 union ic, {y(t)});

Question 4(c)
> ode1 := {diff(y(t),t,t) + 2*diff(y(t),t) + 5*y(t) = piecewise(t<=Pi,sin(2*t),0)}:
> ic := {y(0)=0, D(y)(0)=0}:
> dsolve(ode1 union ic, {y(t)});

> simplify(%);

Question 6(c)
> laplace(abs(sin(w*t)),t,s);