73.3.14 problem 4.4 (d)

Internal problem ID [15048]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (d)
Date solved : Tuesday, January 28, 2025 at 07:28:37 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.392 (sec). Leaf size: 55

DSolve[D[y[x],x]==(y[x]^2+1)/(x^2+1),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 ]\left [\int _1^x\frac {1}{K[2]^2+1}dK[2]+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}