Internal problem ID [8572]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 992.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }+F \relax (x ) \left (-7 x y^{2}-x^{3}\right )-\frac {y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x) = -F(x)*(-7*x*y(x)^2-x^3)+y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\left (\int F \relax (x ) x^{2}d x +c_{1}\right ) \sqrt {7}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 0.24 (sec). Leaf size: 37
DSolve[y'[x] == y[x]/x - F[x]*(-x^3 - 7*x*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (\sqrt {7} \left (\int _1^xF(K[1]) K[1]^2dK[1]+c_1\right )\right )}{\sqrt {7}} \\ \end{align*}