73.7.29 problem 29

Internal problem ID [15187]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 07:40:44 AM
CAS classification : [_quadrature]

\begin{align*} y^{2}+1-y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve(y(x)^2+1-diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 41

DSolve[y[x]^2+1-D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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