63.4.3 problem 1(c)

Internal problem ID [13046]
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 : Tuesday, January 28, 2025 at 04:50:06 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 41

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