72.2.29 problem 22

Internal problem ID [14664]
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
Date solved : Tuesday, January 28, 2025 at 06:46:50 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} v^{\prime }&=2 V \left (t \right )-2 v \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(v(t),t)=(V(t)-v(t))/(1/2*1),v(t), singsol=all)
 

\[ v = \left (2 \left (\int V \left (t \right ) {\mathrm e}^{2 t}d t \right )+c_{1} \right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 32

DSolve[D[ v[t],t]==(V[t]-v[t])/(1/2*1),v[t],t,IncludeSingularSolutions -> True]
 

\[ v(t)\to e^{-2 t} \left (\int _1^t2 e^{2 K[1]} V(K[1])dK[1]+c_1\right ) \]