11assgnA09.html

11assgnA09.mws

For MATH 333 Assignment #11 3.3: 23, 24 -- 11assgnA09.mws

"Find the general real-valued solution of each ODE. Plot solution curves in the -plane for

-1 <= <= 5, where , y'(0) = -6, -3, 0, 3, 6. Plot the corresponding orbits in a rectangle that shows their main features."

> restart;

> with(DEtools, DEplot):

Common Initial-Value Stuff

> TRG := t=-1..5:

> yZRO := 1: ypZROlist := [-6, -3, 0, 3, 6]:

> PTS := map( x -> [1,x], ypZROlist);

> IClist := map(x -> [y(0)=1, D(y)(0) = x], ypZROlist);

> ICyvLIST := map(x -> [y(0)=1, v(0) = x], ypZROlist);

3.3: 23

The five solution curves:

> DE23 := (D@@2)(y)(t) + D(y)(t) = 0:

> DE := DE23;

> IVPlist := map(q -> {DE,op(q)}, IClist):

> solnLIST := map( u -> dsolve(u, y(t)), IVPlist ):

> plotLIST := map(z -> plot(rhs(z), TRG) ,solnLIST):

> plots[display](plotLIST);

The orbits:

> RHS := solve( DE, (D@@2)(y)(t)):

> RHS := subs(D(y)(t) = v(t), RHS):

> DEA := D(y)(t) = v(t);

> DEB := D(v)(t) = RHS;

> SYS := {DEA, DEB};

> DEplot(SYS, [y(t), v(t)], TRG, ICyvLIST, stepsize=0.05);

>

>

3.3: 24

The five solution curves:

> DE24 := (D@@2)(y)(t) + 2*D(y)(t) + 65*y(t)= 0:

> DE := DE24;

> IVPlist := map(q -> {DE,op(q)}, IClist):

> solnLIST := map( u -> dsolve(u, y(t)), IVPlist ):

> plotLIST := map(z -> plot(rhs(z), TRG) ,solnLIST):

> plots[display](plotLIST);

The orbits:

> RHS := solve( DE, (D@@2)(y)(t)):

> RHS := subs(D(y)(t) = v(t), RHS):

> DEA := D(y)(t) = v(t);

> DEB := D(v)(t) = RHS;

> SYS := {DEA, DEB};

> DEplot(SYS, [y(t), v(t)], TRG, ICyvLIST, stepsize=0.05);

>