Internal problem ID [9855]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, section 1.2. Riccati Equation. subsection 1.2.8-1. Equations containing arbitrary
functions (but not containing their derivatives).
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2} f \relax (x )-a n \,x^{n -1}+a^{2} x^{2 n} f \relax (x )=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)=f(x)*y(x)^2+a*n*x^(n-1)-a^2*x^(2*n)*f(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y'[x]==f[x]*y[x]^2+a*n*x^(n-1)-a^2*x^(2*n)*f[x],y[x],x,IncludeSingularSolutions -> True]
Not solved