Internal problem ID [5758]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations
problems. page 12
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y+\sqrt {y x}-y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve((y(x)+sqrt(x*y(x)))-x*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {y \left (x \right )}{\sqrt {y \left (x \right ) x}}+\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 17
DSolve[(y[x]+Sqrt[x*y[x]])-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \]