72.5.20 problem 7

Internal problem ID [14706]
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 : Tuesday, January 28, 2025 at 07:12:08 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[ v[t],t]==-v[t]^2-2*v[t]-2,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*}