Internal problem ID [5016]
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: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y+\left (2 \sqrt {x y}-x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 18
dsolve(y(x)+(2*sqrt(x*y(x))-x)*diff(y(x),x)=0,y(x), singsol=all)
\[ \ln \left (y \relax (x )\right )+\frac {x}{\sqrt {x y \relax (x )}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.231 (sec). Leaf size: 33
DSolve[y[x]+(2*Sqrt[x*y[x]]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(x)}{x}}}+2 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]