# Tag Info

7

I think your initial condition is singular. In order to solve the ODEs, consider $(x(t), y(t))$ as a planar curve, we may try changing the parameter $t$ to the arc length parameter $s$: \left\{\begin{split} \frac{\mathrm{d}x}{\mathrm{d}s}=\frac{x'(t)}{\sqrt{x'(t)^2+y'(t)^2}}\\ \frac{\mathrm{d}y}{\mathrm{d}s}=\frac{y'(t)}{\sqrt{x'(t)^2+y'(t)^2}}\\ ...

5

The problem is that Mathematica prematurely threads r[t] - p not knowing r[t] is actually in $\mathbb{R}^2$ In[]:= r[t]-{0,0} Out[]= {r[t],r[t]} Which is not what you want. A quick fix for these types of issues is to create a function that only evaluates for numerical values (Changed to NDSolve since I only have v8): dummy[r_?(VectorQ[#, NumericQ] ...

5

- update - @whuber gives insightful comment and I agree I should mention here the following. Below we consider a perturbed form (solvable exactly in Bessel functions) of original equation up to linear term. This allows us to understand behavior of the system around t ~ 0. - original - The following shows that under some general assumptions there is no ...

2

Your functions for y and x are single values and not lists, and thus doing a ParametricPlot for the sum of these is not going to work. However, to solve the equations and get a plot you can run the following: alpha = 0.5 beta = 1 solf[b_, c_, tp_] := Module[{sol}, sol = NDSolve[{x'[t] == -x[t]*a[t] - 3*x[t] + alpha*y[t]^2 + 1/2*beta*(r1[t]^2 - ...

2

As an illustration of my initial comment, let's look at various starting points, following @Andrew's method: sols = Table[ NDSolveValue[(2 + Sqrt[2] + s^2 - (-2 + Sqrt[2]) s^4 + s^6)/(1 + s^2)^2 yy[s] - (1 - s^2)^2 yy''[s] == 0 && yy[start] == yy'[start] (start + 1) && yy'[start] == 1, yy[s], {s, start, 1}], {start, -1 + ...

1

As a workaround it is possible to step up a bit from the left end: leftend = -1 + 10^-8; NDSolve[(2 + Sqrt[2] + s^2 - (-2 + Sqrt[2]) s^4 + s^6)/(1 + s^2)^2 yy[s] - (1 - s^2)^2 yy''[s] == 0 && yy[leftend] == 0 && yy'[leftend] == 1, yy[s], {s, leftend, 1}][[1]]

Only top voted, non community-wiki answers of a minimum length are eligible