Re: newbie help

• To: mathgroup at smc.vnet.net
• Subject: [mg107660] Re: [mg107641] newbie help
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 22 Feb 2010 03:08:44 -0500 (EST)

```eqn1 = x'[t] == Sin[x[t]];

sol1 = DSolve[eqn1, x[t], t][[1]] /.
C[1] -> c // Quiet // FullSimplify

{x[t] -> 2*ArcTan[E^(c + t)]}

Verifying that sol1 satisfies the equation eqn1

eqn1 /. Join[sol1, D[sol1, t]] // Simplify

True

p1[t_, c_] = x[t] /. sol1;

eqn2 = x'[t] == x[t]^2;

sol2 = DSolve[eqn2, x[t], t][[1]] /.
C[1] -> c // Simplify

{x[t] -> -(1/(c + t))}

Verifying that sol2 satisfies the equation eqn2

eqn2 /. Join[sol2, D[sol2, t]] // Simplify

True

p2[t_, c_] = x[t] /. sol2;

Manipulate[
Plot[{p1[t, c], p2[t, c]},
{t, -3, 3},
PlotStyle -> {Blue, {Red, Thick}}, PlotRange -> {-3, 3},
Exclusions -> -c,
ExclusionsStyle -> Blue],
{{c, 0}, -1, 1, 0.01,
Appearance -> "Labeled"}]

Bob Hanlon

---- lorrainetx <lorraine.ramos at gpisd.org> wrote:

=============
I've never worked with this program before and I'm having trouble
getting it to do what I want it to do. If there is a good resource to
help translate the math to programing help it would be appreciated.
This is what I'm working on:(I can upload my notebook if it is easier
to help see what I did wrong)
Solve the differential equation x' sin (x).
sol = DSolve[x'[t] == Sin[x[t]], x[t], t] // FullSimplify // Quiet

\[Phi][t_, c_] := x[t] /. sol[[1]] /. C[1] -> c
\[Phi][t, c]

sol = DSolve[x'[t] == x[t]^2, x[t], t] // FullSimplify // Quiet

\[Phi][t_, c_] := x[t] /. sol[[1]] /. C[1] -> c
\[Phi][t, c]

Manipulate[
Plot[{\[Phi][t, c], 0}, {t, -3, 3},
PlotStyle -> {Blue, {Red, Thick}}, PlotRange -> {-3, 3}], {c, -1,
1}]

plot = VectorPlot[{1, x}, {t, 0, 10}, {x, -10, 10},
VectorScale -> 0.04];

Show[plot, Frame -> True, AspectRatio -> Automatic]

My graphs are not working right.

```

• Prev by Date: Digitizing plots with Mathematica (i.e. extracting data points from
• Next by Date: Re: Handheld mathematica
• Previous by thread: Re: newbie help
• Next by thread: Loops in Manipulate