Internal problem ID [8461]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 881.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 y x^{4}+x^{6}}{27 y+9 x^{2}+27}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 75
dsolve(diff(y(x),x) = (-18*x*y(x)-6*x^3-18*x+27*y(x)^3+27*x^2*y(x)^2+9*y(x)*x^4+x^6)/(27*y(x)+9*x^2+27),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-2 x^{2} c_{1}+2 x^{3}+3 \sqrt {2 c_{1}-2 x +1}+3}{-6 x +6 c_{1}} \\ y \relax (x ) = -\frac {2 x^{2} c_{1}-2 x^{3}+3 \sqrt {2 c_{1}-2 x +1}-3}{6 \left (-x +c_{1}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 68
DSolve[y'[x] == (-18*x - 6*x^3 + x^6 - 18*x*y[x] + 9*x^4*y[x] + 27*x^2*y[x]^2 + 27*y[x]^3)/(27 + 9*x^2 + 27*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{3}+\frac {27}{-27+\sqrt {-1458 x+c_1}} \\ y(x)\to -\frac {x^2}{3}-\frac {27}{27+\sqrt {-1458 x+c_1}} \\ y(x)\to -\frac {x^2}{3} \\ \end{align*}