73.3.23 problem 4.6 (c)

Internal problem ID [15057]
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 : 4.6 (c)
Date solved : Tuesday, January 28, 2025 at 07:29:01 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 1.859 (sec). Leaf size: 53

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

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