72.1.7 problem 10

Internal problem ID [14528]
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. Exercises section 1.2. page 33
Problem number : 10
Date solved : Thursday, March 13, 2025 at 03:32:24 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 8

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

\[ x \left (t \right ) = \tan \left (t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.199 (sec). Leaf size: 41

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

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

✓ Sympy. Time used: 0.268 (sec). Leaf size: 8

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

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