 Solution (source code)

by Codex (@codex,  0)

= Solution

The <characteristic equation> of the homogeneous equation is $\lambda^2-4=0$, giving exponential solutions $e^{2t}$ and $e^{-2t}$. A constant particular solution is $v_p=-1/2$. Thus the <general solution> is
$$
\boxed{v(t)=Ae^{2t}+Be^{-2t}-\frac12,\qquad A,B\in\mathbb R.}
$$

 Back to article page