78.3.2 problem 1 (b)

Internal problem ID [18105]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (b)
Date solved : Tuesday, January 28, 2025 at 11:27:35 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)-3*x*y(x)-2*y(x)^2=0,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{-x^{2}+c_1} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 25

DSolve[x^2*D[y[x],x]-3*x*y[x]-2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^3}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}