Internal problem ID [8479]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 899.
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 {32 x^{5}+64 x^{6}+64 x^{6} y^{2}+32 y x^{4}+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 y x^{2}+1}{64 x^{8}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve(diff(y(x),x) = 1/64*(32*x^5+64*x^6+64*y(x)^2*x^6+32*y(x)*x^4+4*x^2+64*x^6*y(x)^3+48*x^4*y(x)^2+12*x^2*y(x)+1)/x^8,y(x), singsol=all)
\[ y \relax (x ) = \frac {116 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right ) x +3 x c_{1}-1\right ) x^{2}-12 x^{2}-9}{36 x^{2}} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 106
DSolve[y'[x] == (1/64 + x^2/16 + x^5/2 + x^6 + (3*x^2*y[x])/16 + (x^4*y[x])/2 + (3*x^4*y[x]^2)/4 + x^6*y[x]^2 + x^6*y[x]^3)/x^8,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\&,\frac {\log \left (\frac {\frac {3 y(x)}{x^2}+\frac {4 x^2+3}{4 x^4}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^6}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\&\right ]=-\frac {1}{9} 29^{2/3} \left (\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ] \]