15.2.10 problem 10

Internal problem ID [2880]
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 : 10
Date solved : Monday, January 27, 2025 at 06:23:22 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 71

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

\[ \frac {y c_1 \,x^{2}-y \sqrt {x y}\, c_1 x -c_1 \,x^{3}+\sqrt {x y}\, c_1 \,x^{2}+x +\sqrt {x y}}{\left (-x +y\right ) \left (\sqrt {x y}-x \right ) x} = 0 \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 26

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

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