Internal problem ID [8555]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 975.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-y^{3}-y^{2} x^{2}-\frac {y x^{4}}{3}-\frac {x^{6}}{27}+\frac {2 x}{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 59
dsolve(diff(y(x),x) = y(x)^3+x^2*y(x)^2+1/3*y(x)*x^4+1/27*x^6-2/3*x,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2} \sqrt {-54 c_{1}-2 x}-3}{3 \sqrt {-54 c_{1}-2 x}} \\ y \relax (x ) = -\frac {x^{2} \sqrt {-54 c_{1}-2 x}+3}{3 \sqrt {-54 c_{1}-2 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.179 (sec). Leaf size: 58
DSolve[y'[x] == (-2*x)/3 + x^6/27 + (x^4*y[x])/3 + x^2*y[x]^2 + y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{3}-\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {x^2}{3}+\frac {1}{\sqrt {-2 x+c_1}} \\ y(x)\to -\frac {x^2}{3} \\ \end{align*}