1.8 problem 3.2

Internal problem ID [3854]

Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 3.2.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]

Solve \begin {gather*} \boxed {\left (2 \sqrt {y x}-x \right ) y^{\prime }+y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

dsolve((2*sqrt(x*y(x))-x)*diff(y(x),x)+y(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: 0.253 (sec). Leaf size: 33

DSolve[(2*Sqrt[x*y[x]]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(x)}{x}}}+2 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]