Suppose that a particle moves along an $\small{s}$-axis. Using ds/dt for the first derivative and d2s/dt2 for the second derivative, find differential equations whose solution is $\small{s(t)}$ if:

(a) The particle's velocity $\small{v(t)}$ is always one-third of $\small{s(t)}$.

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(b) The particle's acceleration $\small{a(t)}$ is always seven times its velocity.

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