Internal problem ID [10610]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime } x -y^{2} f \left (x \right )-n y=x^{2 n} f \left (x \right ) a} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 35
dsolve(x*diff(y(x),x)=f(x)*y(x)^2+n*y(x)+a*x^(2*n)*f(x),y(x), singsol=all)
\[ y \left (x \right ) = -\tan \left (-\sqrt {a}\, \left (\int \frac {x^{n} f \left (x \right )}{x}d x \right )+c_{1} \right ) \sqrt {a}\, x^{n} \]
✓ Solution by Mathematica
Time used: 0.577 (sec). Leaf size: 41
DSolve[x*y'[x]==f[x]*y[x]^2+n*y[x]+a*x^(2*n)*f[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {a} x^n \tan \left (\sqrt {a} \int _1^xf(K[1]) K[1]^{n-1}dK[1]+c_1\right ) \]