Internal problem ID [8567]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 987.
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 (-a \,x^{2}+y^{2}\right )-\frac {y}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x) = -F(x)*(-a*x^2+y(x)^2)+y(x)/x,y(x), singsol=all)
\[ y \relax (x ) = \tanh \left (\left (\int F \relax (x ) x d x \right ) \sqrt {a}+c_{1} \sqrt {a}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 2.264 (sec). Leaf size: 35
DSolve[y'[x] == y[x]/x - F[x]*(-(a*x^2) + y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {a} x \tanh \left (\sqrt {a} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right ) \\ \end{align*}