72.1.7 problem 10

Internal problem ID [14607]
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 : Tuesday, January 28, 2025 at 06:44:19 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==1+x[t]^2,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*}