Internal problem ID [8473]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 893.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x),G(x)]], _Abel]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 x^{2} y^{2}+12 x y+8}{x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 41
dsolve(diff(y(x),x) = (6*x+x^3+x^3*y(x)^2+4*x^2*y(x)+x^3*y(x)^3+6*x^2*y(x)^2+12*x*y(x)+8)/x^3,y(x), singsol=all)
\[ y \relax (x ) = \frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right ) x -3 x -18}{9 x} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 80
DSolve[y'[x] == (8 + 6*x + x^3 + 12*x*y[x] + 4*x^2*y[x] + 6*x^2*y[x]^2 + x^3*y[x]^2 + x^3*y[x]^3)/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {3 y(x)+\frac {x+6}{x}}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ] \]