28.1.95 problem 117

Internal problem ID [4401]
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
Date solved : Monday, January 27, 2025 at 09:14:36 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} 2 \sqrt {y x}-y-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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: 0.221 (sec). Leaf size: 26

DSolve[(2*Sqrt[x*y[x]]-y[x])-x*D[y[x],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*}