72.2.29 problem 22

Internal problem ID [14585]
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 : Thursday, March 13, 2025 at 03:37:50 AM
CAS classification : [[_linear, `class A`]]

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

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

ode:=diff(v(t),t) = 2*V(t)-2*v(t); 
dsolve(ode,v(t), singsol=all);
 

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

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

ode=D[ v[t],t]==(V[t]-v[t])/(1/2*1); 
ic={}; 
DSolve[{ode,ic},v[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.700 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
v = Function("v") 
ode = Eq(-2*V(t) + 2*v(t) + Derivative(v(t), t),0) 
ics = {} 
dsolve(ode,func=v(t),ics=ics)
 

\[ - 2 \int V{\left (t \right )} e^{2 t}\, dt + 2 \int v{\left (t \right )} e^{2 t}\, dt = C_{1} \]