8.5.3 problem 3

Internal problem ID [731]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 3
Date solved : Monday, January 27, 2025 at 02:59:46 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x*diff(y(x),x) = y(x)+2*(x*y(x))^(1/2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 19

DSolve[x*D[y[x],x] == y[x]+2*(x*y[x])^(1/2),y[x],x,IncludeSingularSolutions -> True]
 

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