48.1.8 problem Example 3.8

Internal problem ID [7509]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page 114
Problem number : Example 3.8
Date solved : Monday, January 27, 2025 at 03:03:07 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.162 (sec). Leaf size: 19

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

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