73.7.9 problem 9

Internal problem ID [15167]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 07:39:36 AM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]

\begin{align*} x y^{2}-6+x^{2} y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(x*y(x)^2-6+x^2*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {\sqrt {12 x +c_{1}}}{x} \\ y &= -\frac {\sqrt {12 x +c_{1}}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 38

DSolve[x*y[x]^2-6+x^2*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {12 x+c_1}}{x} \\ y(x)\to \frac {\sqrt {12 x+c_1}}{x} \\ \end{align*}