Internal problem ID [3799]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 547.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {x \left (-2 y+x \right ) y^{\prime }+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve(x*(x-2*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1} x -\sqrt {c_{1}^{2} x^{2}+4 c_{1} x}}{2 c_{1}} y \left (x \right ) = \frac {c_{1} x +\sqrt {c_{1}^{2} x^{2}+4 c_{1} x}}{2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 5.122 (sec). Leaf size: 92
DSolve[x(x-2 y[x])y'[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {x \left (x-4 e^{c_1}\right )}\right ) y(x)\to \frac {1}{2} \left (x+\sqrt {x \left (x-4 e^{c_1}\right )}\right ) y(x)\to 0 y(x)\to \frac {1}{2} \left (x-\sqrt {x^2}\right ) y(x)\to \frac {1}{2} \left (\sqrt {x^2}+x\right ) \end{align*}