How do you use DSolve with Vector?

Question

I'm trying to create an ODE for motion in 2 dimensions. What I have so far is:

x0 = {1.5, -4.}; 
v = {0, 8}; 
DSolve[{x'[t] == v, x[0] == x0}, x[t], t]

This works with one dimension, but when I try and expand the idea for a vector/matrix, I get:

DSolve::nolist: List encountered within {(x^\[Prime])[t]=={0,8}}. There should be no lists on either side of the equations.

How do I fix this?

NDSolve works without problems: NDSolve[{x'[t] == {0, 8}, x[0] == {1.5, -4.}}, x , {t, 0, 1}] — Ulrich Neumann, Dec 22 '19 at 15:56
Yeah, I haven't quite figured out why NDSolve is smart enough to deal with a list, but DSolve can't. — Quark Soup, Dec 22 '19 at 16:01

Bill Watts · Accepted Answer · 2019-12-22T00:56:11.070

5

MMa doesn't know x[t] is a vector, so try this.

x0 = {1.5, -4.};
v = {0, 8};
x[t_] = {x1[t], x2[t]}

eq = x'[t] == v // Thread
(*{x1'[t] == 0, x2'[t] == 8}*)

init = x[0] == x0 // Thread
(*{x1[0] == 1.5, x2[0] == -4.}*)

DSolve[{eq, init}, x[t], t]
(*{{x1[t] -> 1.5, x2[t] -> 8 t - 4.}}*)

x[t] /. %
(*{{1.5, 8 t - 4.}}*)

edited Dec 22 '19 at 00:56

answered Dec 21 '19 at 23:33

Bill Watts

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This doesn't work. The velocity equation resolves to ${Derivative[1][x][t] == 0, Derivative[1][x][t] == 8}$ and thus DSolve doesn't have enough dependent variables to solve. – Quark Soup Dec 22 '19 at 00:42
The threading doesn't do what your comments suggest they should do. – Quark Soup Dec 22 '19 at 00:54
Corrected. I had mistakenly commented out the x[t] equation. Now changed the init to x0. Should work for you. – Bill Watts Dec 22 '19 at 00:58
1

You must not have the x array assigned. – Bill Watts Dec 22 '19 at 02:31
1

@Quarkly it worked for me – b3m2a1 Dec 22 '19 at 10:36
OK. It does work now. Thank you. – Quark Soup Dec 22 '19 at 14:13

How do you use DSolve with Vector?

1 Answers1