Internal problem ID [9636]
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: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x^{2} y^{\prime }-y^{2} c \,x^{2}-\left (x^{n} a +b \right ) x y-\alpha \,x^{2 n}-\beta \,x^{n}-\gamma =0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 1036
dsolve(x^2*diff(y(x),x)=c*x^2*y(x)^2+(a*x^n+b)*x*y(x)+alpha*x^(2*n)+beta*x^n+gamma,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 2.16 (sec). Leaf size: 2380
DSolve[x^2*y'[x]==c*x^2*y[x]^2+(a*x^n+b)*x*y[x]+\[Alpha]*x^(2*n)+\[Beta]*x^n+\[Gamma],y[x],x,IncludeSingularSolutions -> True]
Too large to display