Internal problem ID [1902]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-\sqrt {y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)-y(x)=sqrt(x*y(x)),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: 0.165 (sec). Leaf size: 17
DSolve[x*y'[x]-y[x]==Sqrt[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \\ \end{align*}