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: 0.015 (sec). Leaf size: 71
dsolve((2*sqrt(x*y(x))-y(x))-x*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {x^{2} c_{1} y \left (x \right )-y \left (x \right ) \sqrt {x y \left (x \right )}\, c_{1} x -c_{1} x^{3}+\sqrt {x y \left (x \right )}\, c_{1} x^{2}+x +\sqrt {x y \left (x \right )}}{\left (-x +y \left (x \right )\right ) \left (\sqrt {x y \left (x \right )}-x \right ) x} = 0 \]
✓ 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*}