Internal problem ID [12607]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {v^{\prime }-\frac {K -v}{R C}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(v(t),t)=(K-v(t))/(R*C),v(t), singsol=all)
\[ v \left (t \right ) = K +c_{1} {\mathrm e}^{-\frac {t}{R C}} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 26
DSolve[v'[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*}