Internal problem ID [3219]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 473.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x^{3}+2 y\right ) y^{\prime }-3 x \left (2-y x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 51
dsolve((x^3+2*y(x))*diff(y(x),x) = 3*x*(2-x*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{3}}{2}-\frac {\sqrt {x^{6}+12 x^{2}-4 c_{1}}}{2} \\ y \relax (x ) = -\frac {x^{3}}{2}+\frac {\sqrt {x^{6}+12 x^{2}-4 c_{1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 65
DSolve[(x^3+2 y[x])y'[x]==3 x(2 - x y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-x^3-\sqrt {x^6+12 x^2+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-x^3+\sqrt {x^6+12 x^2+4 c_1}\right ) \\ \end{align*}