73.3.47 problem 4.8 (f)

Internal problem ID [15081]
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 : 4.8 (f)
Date solved : Tuesday, January 28, 2025 at 07:30:02 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 15

dsolve([diff(y(x),x)=(y(x)^2-1)/(x*y(x)),y(1) = -2],y(x), singsol=all)
 

\[ y = -\sqrt {3 x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 18

DSolve[{D[y[x],x]==(y[x]^2-1)/(x*y[x]),{y[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {3 x^2+1} \]