73.3.13 problem 4.4 (c)

Internal problem ID [15047]
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 (c)
Date solved : Tuesday, January 28, 2025 at 07:28:34 AM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }&=y^{2}+9 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

dsolve(x*y(x)*diff(y(x),x)=y(x)^2+9,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {c_{1} x^{2}-9} \\ y &= -\sqrt {c_{1} x^{2}-9} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.404 (sec). Leaf size: 57

DSolve[x*y[x]*D[y[x],x]==y[x]^2+9,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-9+e^{2 c_1} x^2} \\ y(x)\to \sqrt {-9+e^{2 c_1} x^2} \\ y(x)\to -3 i \\ y(x)\to 3 i \\ \end{align*}