Internal problem ID [1902]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 6, page 25
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {-y+y^{\prime } x -\sqrt {y x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*diff(y(x),x)-y(x)=sqrt(x*y(x)),y(x), singsol=all)
\[ -\frac {y \left (x \right )}{\sqrt {x y \left (x \right )}}+\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.162 (sec). Leaf size: 17
DSolve[x*y'[x]-y[x]==Sqrt[x*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x (\log (x)+c_1){}^2 \]