Find the (v(t)) that satisfies the following differential equation and initial conditions: [ begin{gathered} frac{d^{2} v(t)}{d t^{2}}+10

Question:

Find the $v(t)$ that satisfies the following differential equation and initial conditions:

\[
\begin{gathered}
\frac{d^{2} v(t)}{d t^{2}}+10 \frac{d v(t)}{d t}+125 v(t)=250 u(t) \\
v(0)=5 \mathrm{~V}, \frac{d v(0)}{d t}=25 \mathrm{~V} / \mathrm{s}
\end{gathered}
\]

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