Internal problem ID [3280]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 536.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (2 x^{3}+y\right ) y^{\prime }-6 y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 227
dsolve(x*(2*x^3+y(x))*diff(y(x),x) = 6*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = x^{3} \left (\frac {x^{3}-\sqrt {x^{6}+8 x^{3} c_{1}}}{2 c_{1}}+2\right ) \\ y \relax (x ) = x^{3} \left (\frac {x^{3}+\sqrt {x^{6}+8 x^{3} c_{1}}}{2 c_{1}}+2\right ) \\ y \relax (x ) = x^{3} \left (\frac {\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right )^{3} \left (x^{3}-\sqrt {x^{6}+8 x^{3} c_{1}}\right )}{2 c_{1}}+2\right ) \\ y \relax (x ) = x^{3} \left (\frac {\left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right )^{3} \left (x^{3}+\sqrt {x^{6}+8 x^{3} c_{1}}\right )}{2 c_{1}}+2\right ) \\ y \relax (x ) = x^{3} \left (\frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right )^{3} \left (x^{3}-\sqrt {x^{6}+8 x^{3} c_{1}}\right )}{2 c_{1}}+2\right ) \\ y \relax (x ) = x^{3} \left (\frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right )^{3} \left (x^{3}+\sqrt {x^{6}+8 x^{3} c_{1}}\right )}{2 c_{1}}+2\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.237 (sec). Leaf size: 123
DSolve[x(2 x^3+y[x])y'[x]==6 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x^3 \left (-1+\frac {2}{1-\frac {4 x^{3/2}}{\sqrt {16 x^3+c_1}}}\right ) \\ y(x)\to 2 x^3 \left (-1+\frac {2}{1+\frac {4 x^{3/2}}{\sqrt {16 x^3+c_1}}}\right ) \\ y(x)\to 0 \\ y(x)\to 2 x^3 \\ y(x)\to \frac {2 \left (\left (x^3\right )^{3/2}-x^{9/2}\right )}{x^{3/2}+\sqrt {x^3}} \\ \end{align*}