Internal problem ID [8477]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 897.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class C]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (-108 y x^{\frac {3}{2}}+18 x^{\frac {9}{2}}-108 x^{\frac {3}{2}}-216 y^{3}+108 y^{2} x^{3}-18 y x^{6}+x^{9}\right ) \sqrt {x}}{-216 y+36 x^{3}-216}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 85
dsolve(diff(y(x),x) = (-108*x^(3/2)*y(x)+18*x^(9/2)-108*x^(3/2)-216*y(x)^3+108*x^3*y(x)^2-18*y(x)*x^6+x^9)*x^(1/2)/(-216*y(x)+36*x^3-216),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {9 c_{1}-12 x^{\frac {3}{2}}}\, x^{3}-3 x^{3}+18}{6 \sqrt {9 c_{1}-12 x^{\frac {3}{2}}}-18} \\ y \relax (x ) = \frac {\sqrt {9 c_{1}-12 x^{\frac {3}{2}}}\, x^{3}+3 x^{3}-18}{6 \sqrt {9 c_{1}-12 x^{\frac {3}{2}}}+18} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.038 (sec). Leaf size: 76
DSolve[y'[x] == (Sqrt[x]*(-108*x^(3/2) + 18*x^(9/2) + x^9 - 108*x^(3/2)*y[x] - 18*x^6*y[x] + 108*x^3*y[x]^2 - 216*y[x]^3))/(-216 + 36*x^3 - 216*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{6}-\frac {216}{216+\sqrt {-62208 x^{3/2}+c_1}} \\ y(x)\to \frac {x^3}{6}+\frac {216}{-216+\sqrt {-62208 x^{3/2}+c_1}} \\ y(x)\to \frac {x^3}{6} \\ \end{align*}