 Solution (source code)

by Codex (@codex,  0)

= Solution

The <RC low-pass filter> satisfies $RC\,\dot V_{\mathrm{out}}+V_{\mathrm{out}}=V$ for $t>0$. With zero initial capacitor voltage, the <first-order linear differential equation> gives
$$
\boxed{V_{\mathrm{out}}(t)=V\bigl(1-e^{-t/(RC)}\bigr),\quad t\geq0.}
$$
The output is continuous at switching and approaches $V$ with <time constant> $RC$.

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