Internal problem ID [9322]
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]
\[ \boxed {y^{\prime }+F \left (x \right ) \left (-a \,x^{2}+y^{2}\right )-\frac {y}{x}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(diff(y(x),x) = -F(x)*(-a*x^2+y(x)^2)+y(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \tanh \left (\left (\int F \left (x \right ) x d x \right ) \sqrt {a}+c_{1} \sqrt {a}\right ) x \sqrt {a} \]
✓ Solution by Mathematica
Time used: 4.668 (sec). Leaf size: 35
DSolve[y'[x] == y[x]/x - F[x]*(-(a*x^2) + y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {a} x \tanh \left (\sqrt {a} \left (\int _1^xF(K[1]) K[1]dK[1]+c_1\right )\right ) \]