Internal problem ID [8478]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 898.
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 {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 y x^{2}+1}{16 x^{6} \left (4 y x^{2}+1+4 x^{2}\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 83
dsolve(diff(y(x),x) = 1/16/x^6*(32*x^5*y(x)+8*x^3+32*x^5+64*x^6*y(x)^3+48*x^4*y(x)^2+12*x^2*y(x)+1)/(4*x^2*y(x)+1+4*x^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {-4 x^{2}+\sqrt {\frac {x c_{1}+2}{x}}-1}{4 x^{2} \left (\sqrt {\frac {x c_{1}+2}{x}}-1\right )} \\ y \relax (x ) = -\frac {4 x^{2}+\sqrt {\frac {x c_{1}+2}{x}}+1}{4 x^{2} \left (\sqrt {\frac {x c_{1}+2}{x}}+1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.729 (sec). Leaf size: 106
DSolve[y'[x] == (1/16 + x^3/2 + 2*x^5 + (3*x^2*y[x])/4 + 2*x^5*y[x] + 3*x^4*y[x]^2 + 4*x^6*y[x]^3)/(x^6*(1 + 4*x^2 + 4*x^2*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {256 x^2-\sqrt {\frac {8192}{x}+c_1}+64}{4 x^2 \left (-64+\sqrt {\frac {8192}{x}+c_1}\right )} \\ y(x)\to -\frac {256 x^2+\sqrt {\frac {8192}{x}+c_1}+64}{4 x^2 \left (64+\sqrt {\frac {8192}{x}+c_1}\right )} \\ y(x)\to -\frac {1}{4 x^2} \\ \end{align*}