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]
\[ \boxed {y^{\prime } x -y-2 \sqrt {y x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x) = y(x)+2*(x*y(x))^(1/2),y(x), singsol=all)
\[ -\frac {y \left (x \right )}{\sqrt {x y \left (x \right )}}+\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 19
DSolve[x*y'[x] == y[x]+2*(x*y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x (2 \log (x)+c_1){}^2 \]