Internal problem ID [5005]
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]
Solve \begin {gather*} \boxed {y+\sqrt {y x}-x y^{\prime }=0} \end {gather*}
✓ 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)
\[ -\frac {y \relax (x )}{\sqrt {x y \relax (x )}}+\frac {\ln \relax (x )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.279 (sec). Leaf size: 17
DSolve[(y[x]+Sqrt[x*y[x]])-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \\ \end{align*}