72.5.20 problem 7

Internal problem ID [14627]
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 1.6 page 89
Problem number : 7
Date solved : Thursday, March 13, 2025 at 04:10:45 AM
CAS classification : [_quadrature]

\begin{align*} v^{\prime }&=-v^{2}-2 v-2 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

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

\[ v = -1-\tan \left (t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.217 (sec). Leaf size: 47

ode=D[ v[t],t]==-v[t]^2-2*v[t]-2; 
ic={}; 
DSolve[{ode,ic},v[t],t,IncludeSingularSolutions->True]
 

\begin{align*} v(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+2 K[1]+2}dK[1]\&\right ][-t+c_1] \\ v(t)\to -1-i \\ v(t)\to -1+i \\ \end{align*}

✓ Sympy. Time used: 0.282 (sec). Leaf size: 8

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

\[ v{\left (t \right )} = \tan {\left (C_{1} - t \right )} - 1 \]