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Huy
11:52 AM
AsymptoticDSolveValue[{x'[t] == -y[t]^3, y'[t] == x[t]^3, x[0] == 1,
y[0] == 0}, x[t], {t, 0, 10}]

Does anyone know why this just returns the same command again? I can compute the Taylor series by hand using this system of DEs, but it is very cumbersome, so I wanted to use Mathematica for help.
nevermind, I found out
AsymptoticDSolveValue[{x'[t] == -y[t]^3, y'[t] == x[t]^3, x[0] == 1,
y[0] == 0}, {x[t], y[t]}, {t, 0, 5}]

this works correctly, however for n>5, I get "indeterminate expression ComplexInfinity + ComplexInfinity encountered" - any idea why?
 
 
2 hours later…
2:08 PM
Over-analyzing quantified self data, I suspect mt doctor is not thrilled if I start explaining my blood pressure with such graphs.
 
 
1 hour later…
3:34 PM
@kirma I imagine he'll ask how often you have fits :)
 
3:51 PM
@C.E. Curve fits are the worst!
 
 
4 hours later…
8:02 PM
@Huy when mma returns same command it means it could not solve it. Here is the solution using Maple fyi:

Order := 10;
dsolve([diff(x(t),t)=-y(t)^3,diff(y(t),t)=x(t)^3,x(0)=1,y(0)=0],[x(t),y(t)],'series',t=0)

which gives

{x(t) = 1 - 1/4*t^4 + 9/160*t^8 + O(t^10), y(t) = t - 3/20*t^5 + 19/480*t^9 + O(t^10)}
 
Huy
8:19 PM
@Nasser thanks. can Maple also compute higher orders?
 
8:41 PM
@Huy yes of course, just change the `Order` variable like this

Order := 30;
dsolve([diff(x(t),t)=-y(t)^3,diff(y(t),t)=x(t)^3,x(0)=1,y(0)=0],[x(t),y(t)],'series',t=0)

{x(t) = 1 - 1/4*t^4 + 9/160*t^8 - 149/9600*t^12 + 15147/3328000*t^16 - 4679969/3394560000*t^20 + 3858173/9052160000*t^24 - 42456658421/317730816000000*t^28 + O(t^30), y(t) = t - 3/20*t^5 + 19/480*t^9 - 469/41600*t^13 + 189611/56576000*t^17 - 1157629/1131520000*t^21 + 215795207/678912000000*t^25 - 307125703061/3071397888000000*t^29 + O(t^30)}
 
Huy
8:52 PM
yes, I'm wondering why
thanks for your help
 
@kirma :D
 
 
1 hour later…
10:32 PM
Anyone have a good QA for rendering 3D arrows that don't get occluded by what they're intersecting? Like I have a 3D coordinate arrow system drawn and when a vector I draw intersects with the coordinate arrows it gets partially occluded & I'd rather it overlap & appear on top...Epilog only does 2D graphics after the fact
 

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