7.5.3 problem 3

Internal problem ID [107]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 3
Date solved : Friday, February 07, 2025 at 07:49:52 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 19

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

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