15.2.3 problem 3

Internal problem ID [2873]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 3
Date solved : Monday, January 27, 2025 at 06:21:23 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

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

\[ -\frac {y}{\sqrt {x y}}+\frac {\ln \left (x \right )}{2}-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.167 (sec). Leaf size: 17

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

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