Internal problem ID [3396]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 23
Problem number: 657.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }-6 y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 31
dsolve(x*(x^3-3*x^3*y(x)+4*y(x)^2)*diff(y(x),x) = 6*y(x)^3,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-3 \,{\mathrm e}^{\textit {\_Z}} x^{3}+6 x^{3} c_{1}+\textit {\_Z} \,x^{3}+2 \,{\mathrm e}^{2 \textit {\_Z}}\right )} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 27
DSolve[x(x^3-3 x^3 y[x]+4 y[x]^2)y'[x]==6 y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^2}{x^3}+\frac {1}{2} (\log (y(x))-3 y(x))=c_1,y(x)\right ] \]