Internal problem ID [3291]
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]]
Solve \begin {gather*} \boxed {x \left (x -2 y\right ) y^{\prime }+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(x*(x-2*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-c_{1} x +\sqrt {x^{2} c_{1}^{2}+4 c_{1} x}}{2 c_{1}} \\ y \relax (x ) = \frac {c_{1} x +\sqrt {x^{2} c_{1}^{2}+4 c_{1} x}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.992 (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*}