62.9.1 problem Ex 1

Internal problem ID [12832]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:25:59 AM
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: 0.144 (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*}