Internal problem ID [3464]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 726.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\left (x -2 \sqrt {y x}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 18
dsolve((x-2*sqrt(x*y(x)))*diff(y(x),x) = y(x),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: 0.218 (sec). Leaf size: 33
DSolve[(x-2 Sqrt[x y[x]])y'[x]==y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(x)}{x}}}+2 \log \left (\frac {y(x)}{x}\right )=-2 \log (x)+c_1,y(x)\right ] \]