Internal problem ID [12608]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {v^{\prime }+2 v=2 V \left (t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(v(t),t)=(V(t)-v(t))/(1/2*1),v(t), singsol=all)
\[ v \left (t \right ) = \left (\int 2 V \left (t \right ) {\mathrm e}^{2 t}d t +c_{1} \right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 32
DSolve[v'[t]==(V[t]-v[t])/(1/2*1),v[t],t,IncludeSingularSolutions -> True]
\[ v(t)\to e^{-2 t} \left (\int _1^t2 e^{2 K[1]} V(K[1])dK[1]+c_1\right ) \]