Internal problem ID [1909]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 6, page 25
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y+y^{\prime } x -2 \sqrt {y x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 58
dsolve(x*diff(y(x),x)+y(x)=2*sqrt(x*y(x)),y(x), singsol=all)
\[ \frac {\sqrt {x y \left (x \right )}}{\left (-x +y \left (x \right )\right ) \left (-x +\sqrt {x y \left (x \right )}\right ) x}+\frac {1}{\left (-x +y \left (x \right )\right ) \left (-x +\sqrt {x y \left (x \right )}\right )}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 26
DSolve[x*y'[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*}