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How to show that if there is two solution of IVP( initial value problem) then it has infinite number of solution?

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If $y_1$ and $y_2$ are solutions that are different at $t_1$, then you can follow backwards the initial value problem with $y(t_1)=y_3$ from any point $y_3$ in the segment $[y_1(t_1),y_2(t_1)]$. As this new solution is bounded by the first two solutions, it can be continued until it meets one of the bounding trajectories, from there continue using those. Thus a new different solution for $y(t_0)=y_0$.

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