78.5.19 problem 4 (h)

Internal problem ID [18162]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 9 (Integrating Factors). Problems at page 80
Problem number : 4 (h)
Date solved : Tuesday, January 28, 2025 at 11:34:38 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 17

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

\[ -2 \sqrt {x y}+y-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 7.702 (sec). Leaf size: 148

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

\begin{align*} y(x)\to 2 x-2 \sqrt {x \left (x-e^{c_1}\right )}-e^{c_1} \\ y(x)\to 2 \left (x+\sqrt {x \left (x-e^{c_1}\right )}\right )-e^{c_1} \\ y(x)\to 2 x-2 \sqrt {x \left (x+e^{c_1}\right )}+e^{c_1} \\ y(x)\to 2 \left (x+\sqrt {x \left (x+e^{c_1}\right )}\right )+e^{c_1} \\ y(x)\to 0 \\ y(x)\to 2 x-2 \sqrt {x^2} \\ y(x)\to 2 \left (\sqrt {x^2}+x\right ) \\ \end{align*}