Internal problem ID [3293]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 549.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (x -2 y\right ) y^{\prime }+\left (2 x -y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 69
dsolve(x*(x-2*y(x))*diff(y(x),x)+(2*x-y(x))*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1}^{2} x^{2}-\sqrt {c_{1}^{4} x^{4}+4 c_{1} x}}{2 x c_{1}^{2}} \\ y \relax (x ) = \frac {c_{1}^{2} x^{2}+\sqrt {c_{1}^{4} x^{4}+4 c_{1} x}}{2 x c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.968 (sec). Leaf size: 114
DSolve[x(x-2 y[x])y'[x]+(2 x - y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\frac {\sqrt {x^3-4 e^{c_1}}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\frac {\sqrt {x^3-4 e^{c_1}}}{\sqrt {x}}\right ) \\ y(x)\to \frac {x}{2}-\frac {\sqrt {x^3}}{2 \sqrt {x}} \\ y(x)\to \frac {x^{3/2}+\sqrt {x^3}}{2 \sqrt {x}} \\ \end{align*}