67.7.29 problem 29

Internal problem ID [16474]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 29
Date solved : Thursday, October 02, 2025 at 01:34:50 PM
CAS classification : [_quadrature]

\begin{align*} y^{2}+1-y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 8

ode:=y(x)^2+1-diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (x +c_1 \right ) \]

✓ Mathematica. Time used: 0.108 (sec). Leaf size: 41

ode=y[x]^2+1-D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.171 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 - Derivative(y(x), x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \tan {\left (C_{1} - x \right )} \]