Internal problem ID [10384]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 1, section 1.2. Riccati Equation. 1.2.2. Equations Containing Power
Functions
Problem number: 54.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x^{2} y^{\prime }-\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}-\left (x^{n} a +b \right ) x y=c \,x^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 215200
dsolve(x^2*diff(y(x),x)=(alpha*x^(2*n)+beta*x^n+gamma)*y(x)^2+(a*x^n+b)*x*y(x)+c*x^2,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 4.676 (sec). Leaf size: 2649
DSolve[x^2*y'[x]==(\[Alpha]*x^(2*n)+\[Beta]*x^n+\[Gamma])*y[x]^2+(a*x^n+b)*x*y[x]+c*x^2,y[x],x,IncludeSingularSolutions -> True]
Too large to display