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Consider the equation $y'=x^3-y^3$.

Prove that every solution of the equation with initial value $y(x_0)=y_0$ can be extended to a solution in $[x_0,+\infty)$ but cannot be extended to a solution in $(-\infty,x_0]$.

Note: $y$ is a function of $x$.

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closed as off-topic by Siminore, Did, M. Winter, Gibbs, José Carlos Santos Jul 6 '18 at 20:35

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    $\begingroup$ just to clarify, y is a function of x so that $y'=\frac {dy}{dx}$? $\endgroup$ – mathreadler Jul 6 '18 at 8:55
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    $\begingroup$ Also please provide some context or attempts at solving the problem. $\endgroup$ – mathreadler Jul 6 '18 at 8:57