##### Hint

If $v(t)$ were equal to $3 e^{7 t}$, is it true that $\diff{v}{t}$ is the same thing as $7v(t)$?

If $v(t)$ were equal to $- 2 e^{7 t}$, is it true that $\diff{v}{t}$ is the same thing as $7v(t)$?

If $v(t)$ were equal to $7 e^{7 t}$, is it true that $\diff{v}{t}$ is the same thing as $7v(t)$?

Any function $v(t)$ where $\diff{v}{t}$ is the same thing as $7v(t)$ is a possible solution, as it obeys the differential equation $\diff{v}{t}=7v(t)$.

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