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Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

2
votes
1answer
Can DSolve give results in parametric form? For example the cycloid equation is: DSolve[{(x'[t])^2 == r/x[t] - 1}, x[t], t] And the solution is usually given in parametric form: $$x=r \,(t- Sin[t …
asked Aug 15 '17 by mattiav27
1
vote
Actually it is not true that DSolve cannot solve it: just consider the uncoupled system formed by the sum $s[t]$ and the difference $d[t]$ of $\Psi_1[t]$ and $\Psi_2[t]$: DSolve[{s''[t] + (e1 + e2 - …
answered Feb 11 '17 by mattiav27
5
votes
1answer
Bug introduced in 8.0 or earlier and fixed in 10.3.0 I am solving With Mathematica 10 the following ODE system: DSolve[{B'[x] == -f[x]*Cos[l]*G[x], G'[x] == +f[x]*Sin[l]*B[x]}, {B,G}, x] The sol …
asked May 31 '15 by mattiav27
2
votes
2answers
How do I extract values from NDSolveValue at particular point: for example how do I extract the last point?
asked Dec 29 '17 by mattiav27
1
vote
2answers
I am in the following situation: I have a complicated ODE for the function f[x] that has no anlytical solution and an integral that depends on f[x]: how can I plot the integral? As a MWE consider the …
asked Jan 16 by mattiav27
0
votes
0answers
I managed to integrate the function F1 given in this post, with ParametricNDSolveVale as follows: f[r_?NumericQ, t_?NumericQ] := h[r] r^3 Cos[2 \[CapitalOmega]k[r] t]; g = ParametricNDSolveValue[{F'[ …
asked Aug 22 by mattiav27
3
votes
1answer
I give Mathematica 10 the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] and I have the following output: {{P -> Function[{x}, C[2] - I Log[C[1] - …
asked Oct 16 '15 by mattiav27
1
vote
0answers
This is a followup question to this question. From these two answers I can build the function sol[r][[1]][t0] as follows: ClearAll["Global`*"] Md = 10^(-9); P = 10; R = 10^4; α = 10^(-2); ϵ = 10^(-4) …
asked Aug 22 by mattiav27