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## Homework Statement

Proof that there exist more than one solution to following equation

[itex]\frac{dx}{dt} = \sqrt[3]{x^{2}} , x(0) = 0[/itex]

## Homework Equations

## The Attempt at a Solution

Well, I need a confirmation to my attempt of solution. The one is quite forward:

[itex]\Rightarrow x=(1/3(t+c))^{3} [/itex]

Pluging in x(0) = 0 yields that:

[itex]\Rightarrow x=(1/3(t))^{3} [/itex] is a solution.

The point is, my professor never told us how to solve ODEs. Most of the time he's talking about manifolds, charts, diffeomorphisms, etc.

So I guess the other solution one finds doing following:

Since [itex]x(0) = 0 \Rightarrow \dot{x}(0) = 0[/itex]

Pluging in [itex]\dot{x}[/itex] one gets:

[itex]0 = \sqrt[3]{x^{2}}[/itex]

and therefore the other solution is x = 0

Are my solutions correct?

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