72.2.27 problem 20

Internal problem ID [14662]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 06:46:48 AM
CAS classification : [_quadrature]

\begin{align*} v^{\prime }&=-\frac {v}{R C} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(v(t),t)=-v(t)/(R*C),v(t), singsol=all)
 

\[ v = c_{1} {\mathrm e}^{-\frac {t}{R C}} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 24

DSolve[D[ v[t],t]==-v[t]/(r*c),v[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} v(t)\to c_1 e^{-\frac {t}{c r}} \\ v(t)\to 0 \\ \end{align*}