63.4.3 problem 1(c)

Internal problem ID [12967]
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 : Wednesday, March 05, 2025 at 08:55:10 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.006 (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: 0.179 (sec). Leaf size: 41

ode=D[y[t],t]==1+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+1}dK[1]\&\right ][t+c_1] \\ y(t)\to -i \\ y(t)\to i \\ \end{align*}

✓ Sympy. Time used: 0.295 (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)
 

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