57.4.3 problem 1(c)

Internal problem ID [14327]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 1(c)
Date solved : Thursday, October 02, 2025 at 09:31:36 AM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 24

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

\begin{align*} y(t)&\to \tan (t+c_1)\\ y(t)&\to -i\\ y(t)&\to i \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 8

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

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