Internal problem ID [81]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x -y-2 \sqrt {y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(x*diff(y(x),x) = y(x)+2*(x*y(x))^(1/2),y(x), singsol=all)
\[ -\frac {y \relax (x )}{\sqrt {x y \relax (x )}}+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.165 (sec). Leaf size: 19
DSolve[x*y'[x] == y[x]+2*(x*y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x (2 \log (x)+c_1){}^2 \\ \end{align*}