Internal problem ID [8394]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 814.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_Abel, 2nd type, class C], [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 38
dsolve(diff(y(x),x) = y(x)/x*(-3*x^3*y(x)-3+y(x)^2*x^7)/(x^3*y(x)+1),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{x^{3} \left (\sqrt {c_{1}-2 x}-1\right )} \\ y \relax (x ) = -\frac {1}{x^{3} \left (\sqrt {c_{1}-2 x}+1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.787 (sec). Leaf size: 75
DSolve[y'[x] == (y[x]*(-3 - 3*x^3*y[x] + x^7*y[x]^2))/(x*(1 + x^3*y[x])),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-x^4+\frac {\sqrt {x (-2 x+1+c_1)}}{\sqrt {\frac {1}{x^7}}}} \\ y(x)\to -\frac {x}{x^4+\frac {\sqrt {x (-2 x+1+c_1)}}{\sqrt {\frac {1}{x^7}}}} \\ y(x)\to 0 \\ \end{align*}