73.5.5 problem 6.3 (a)

Internal problem ID [15116]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.3 (a)
Date solved : Tuesday, January 28, 2025 at 07:33:29 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = \frac {x}{-\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {x}{-\log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}