Internal problem ID [5084]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page
114
Problem number: Example 3.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {x y^{\prime }-2 \sqrt {y x}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*diff(y(x),x)-2*sqrt(x*y(x))=y(x),y(x), singsol=all)
\[ -\frac {y \relax (x )}{\sqrt {x y \relax (x )}}+\ln \relax (x )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.292 (sec). Leaf size: 19
DSolve[x*y'[x]-2*Sqrt[x*y[x]]==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x (2 \log (x)+c_1){}^2 \\ \end{align*}