Internal problem ID [3240]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 117.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {2 \sqrt {y x}-y-x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 58
dsolve((2*sqrt(x*y(x))-y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\sqrt {y \left (x \right ) x}}{\left (y \left (x \right )-x \right ) \left (\sqrt {y \left (x \right ) x}-x \right ) x}+\frac {1}{\left (y \left (x \right )-x \right ) \left (\sqrt {y \left (x \right ) x}-x \right )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 26
DSolve[(2*Sqrt[x*y[x]]-y[x])-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x+e^{\frac {c_1}{2}}\right ){}^2}{x} y(x)\to x \end{align*}