65.3.15 problem 10

Internal problem ID [15652]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:22:02 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 41

ode=D[y[x],x]==1+y[x]^2; 
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: 0.160 (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)
 

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