# Variable name complication with DSolve? [closed]

I'm trying to run the code:

sol = DSolve[{Derivative[1][Subscript[x, 1]][
t] == -(1 - Subscript[w, 1]) x1[t] -
Subscript[σ, 12] Subscript[x, 1][t],
Derivative[1][p][t] == -(1 - Subscript[w, 2]) p[t] +
Subscript[σ, 12] Subscript[x, 1][t],
Subscript[x, 1][0] == 1000, p[0] == 0}, {Subscript[x, 1][t], p[t]},
t]


which is the same as:

sol = DSolve[{Derivative[1][Subscript[x, 1]][
t] == -(1 - w1)*Subscript[x, 1][t] - s12*Subscript[x, 1][t],
Derivative[1][p][t] == -(1 - w2) p[t] + s12 Subscript[x, 1][t],
Subscript[x, 1][0] == 1000, p[0] == 0}, {Subscript[x, 1][t], p[t]},
t]


The only difference is in the name of the variables, the second one gives a solution but not the first.

Also, in the following code:

    Manipulate[
sol = DSolve[{Derivative[1][Subscript[x, 1]][
t] == -(1 - Subscript[w, 1]) x1[t] -
Subscript[σ, 12] Subscript[x, 1][t],
Derivative[1][p][t] == -(1 - Subscript[w, 2]) p[t] +
Subscript[σ, 12] Subscript[x, 1][t],
Subscript[x, 1][0] == 1000, p[0] == 0}, {Subscript[x, 1][t],
p[t]}, t];
Plot[Evaluate[p[t] /. sol[[1, 1]]], {t, 0, 100},
PlotRange -> Automatic], {{Subscript[σ, 12], 0.01,
"Mutation 1->2"}, 0.01,
1}, {{Subscript[w, 2], 0.5,
"Fitness \!$$\*SubscriptBox[\(w$$, $$2$$]\)"}, 0,
2}, {{Subscript[w, 1], 1,
"Fitness \!$$\*SubscriptBox[\(w$$, $$1$$]\)"}, 0, 2}]


If I change all instances of p[t] to Subscript[x,2] it stops working.

Any idea on what's going on?

• In your first expression, you forgot to change one of the x1s. If you change the x1[t] to a Subscript[x, 1][t], then they yield the same results. The same thing in your Manipulate. Commented Jul 7, 2016 at 18:02
• You're right, thank you very much. Commented Jul 7, 2016 at 21:18

As mentioned by March, you didn't change one of the x1[t] terms to Subscript[x, 1][t]

sol = DSolve[{Derivative[1][Subscript[x, 1]][t] ==
-(1 - Subscript[w, 1]) Subscript[x, 1][t] -
Subscript[σ, 12] Subscript[x, 1][t],
Derivative[1][p][t] ==
-(1 - Subscript[w, 2]) p[t] + Subscript[σ, 12] Subscript[x, 1][t],
Subscript[x, 1][0] == 1000, p[0] == 0}, {Subscript[x, 1][t], p[t]}, t]

Manipulate[
sol = DSolve[{Derivative[1][Subscript[x, 1]][
t] == -(1 - Subscript[w, 1]) Subscript[x, 1][t] -
Subscript[σ, 12] Subscript[x, 1][t],
Derivative[1][p][t] == -(1 - Subscript[w, 2]) p[t] +
Subscript[σ, 12] Subscript[x, 1][t],
Subscript[x, 1][0] == 1000, p[0] == 0}, {Subscript[x, 1][t], p[t]}, t];
Plot[Evaluate[p[t] /. sol[[1, 1]]], {t, 0, 100},
PlotRange -> Automatic], {{Subscript[σ, 12], 0.01,
"Mutation 1->2"}, 0.01, 1}, {{Subscript[w, 2], 0.5,
"Fitness \!$$\*SubscriptBox[\(w$$, $$2$$]\)"}, 0,
2}, {{Subscript[w, 1], 1,"Fitness \!$$\*SubscriptBox[\(w$$, $$1$$]\)"}, 0, 2}]