66.8.14 problem 27

Internal problem ID [16065]
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. Review Exercises for chapter 1. page 136
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:40:35 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3+y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(y(t),t) = 3+y(t)^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \sqrt {3}\, \tan \left (\left (c_1 +t \right ) \sqrt {3}\right ) \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 53

ode=D[y[t],t]==3+y[t]^2; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+3}dK[1]\&\right ][t+c_1]\\ y(t)&\to -i \sqrt {3}\\ y(t)&\to i \sqrt {3} \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**2 + Derivative(y(t), t) - 3,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \sqrt {3} \tan {\left (C_{1} - \sqrt {3} t \right )} \]