60.1.136 problem 137

Internal problem ID [10150]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 137
Date solved : Monday, January 27, 2025 at 06:30:06 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 21

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

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