73.5.23 problem 6.7 (k)

Internal problem ID [15134]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (k)
Date solved : Tuesday, January 28, 2025 at 07:36:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 25

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

\[ -\frac {x +y}{\sqrt {x \left (x +y\right )}}+\frac {\ln \left (x \right )}{2}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 26

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

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