48.1.4 problem Example 3.4

Internal problem ID [7505]
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
Date solved : Monday, January 27, 2025 at 03:02:53 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x*diff(y(x),x)-2*sqrt(x*y(x))=y(x),y(x), singsol=all)
 

\[ -\frac {y}{\sqrt {x y}}+\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 19

DSolve[x*D[y[x],x]-2*Sqrt[x*y[x]]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} x (2 \log (x)+c_1){}^2 \]