73.3.33 problem 4.7 (g)

Internal problem ID [15067]
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 : 4.7 (g)
Date solved : Tuesday, January 28, 2025 at 07:29:21 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.231 (sec). Leaf size: 55

DSolve[(x^2+1)*D[y[x],x]==y[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*}