Sample Maple file for Exercises 23 and 24 in Section 3.3 23. Solve 3u''-u'+2u=0 with u(0)=2 and u'(0)=0, then determine the first t at which |u(t)|=10 Solution: First, define and solve the DE: DE23:=3*diff(u(t),t$2)-diff(u(t),t)+2*u(t)=0; U1:=rhs(dsolve({DE23,u(0)=2,D(u)(0)=0},u(t))); We'll plot the solution (with lines at +/-10) to see if we can get an approximate solution, then we'll solve numerically: plot({U1,10,-10},t=0..12); After some plotting, we see the solution is between 10 and 11. Now we'll get an approximate solution: fsolve(U1=-10,t=10..11); EXERCISE 24: Consider 5u''+2u'+7u=0, u(0)=2, u'(0)=1 Solve, and find the smallest T so that |u(t)|<=0.1 for all t>T. DE24:=5*diff(u(t),t$2)+2*diff(u(t),t)+7*u(t)=0; U1:=rhs(dsolve({DE24,u(0)=2,D(u)(0)=1},u(t))); plot({U1,1/10,-1/10},t=0..18); Graphically, it looks like the solution is about 14.5. Now we can solve for it numerically: fsolve(U1=-1/10,t=14..15);