72.2.28 problem 21

Internal problem ID [14663]
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 : 21
Date solved : Tuesday, January 28, 2025 at 06:46:49 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 26

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

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