I always need to laugh when someone says solve does not work, yet they never invested any thought in what they were trying to make those tools do.
I'm not at all surprisd by the way, that solve fails, since it seems unlikely an analytical solution is available for this.
So why did vpasolve fail to do what you want? That just takes ONE thing. A plot.
fplot(delta)
grid on
xline(0);
subs(delta,0)
ans =
0
So it is clear that at delta==0, there is a solution.
vpasolve(delta)
ans =
0
Is there any other solution? It seems that if I force fplot to look over a much wider domain in x, this has the same fundamental shape. It is only when I push the limits on x, for example
fplot(delta,[-100000,100000])
Now it appears that it MIGHT be possible another solution exists. And vpasolve was supposed to know this how? Things seem to happen only for LARGE positive P.
fplot(delta,[0,10000000])
yline(0);
vpasolve(delta,1e6)
ans =
965748.2333617142707833134938588
vpasolve(delta,3e6)
ans =
3022435.2524207491946774838105101
vpasolve is a numerical solver. It often needs an intelligent starting value if you want to see a specific solution. Otherwise, you get pot luck. So, if you want vpasolve to work, then you need to give it even a chance to actually do what you want.
