Find more solutions to the ODE

Asked Nov 18 '17 at 15:03

Active Nov 18 '17 at 16:26

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Consider the IVP, $$x'(t)=f(t,x(t))=x^{2/3},\quad x(1)=0$$ Find 3 solutions to the IVP with domain $[-1,1]$

I separated the variables and solved the ODE, got as a solution $$x(t)=0,~x(t)=\frac{t^3-3t^2+3t-1}{27}$$ How do I find a 3rd solution? $x(t)=0$ solves the IVP trivially. I still need a third solution though.

edited Nov 18 '17 at 16:26

asked Nov 18 '17 at 15:03

1

i have found the same solution as you – Dr. Sonnhard Graubner Nov 18 '17 at 15:41
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Try to consider $x(t) = \left(\frac{t-c}{3}\right)^3$ for $-1< t < c$ and $x(t) = 0$ for $c < t < 1$. – Winther Nov 18 '17 at 16:08
I would say that there are infinitely many solutions, but maybe the piecewise-defined functions count as one. – Tomi27 Nov 18 '17 at 16:19
You can find a similar question here: https://math.stackexchange.com/questions/1015610/numer-of-solutions-for-ivp?rq=1 – Tomi27 Nov 18 '17 at 16:31

Find more solutions to the ODE

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