61.2.54 problem 54

Internal problem ID [12060]
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
Date solved : Tuesday, January 28, 2025 at 06:41:25 PM
CAS classification : [_rational, _Riccati]

\begin{align*} x^{2} y^{\prime }&=\left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \end{align*}

Solution by Maple

Time used: 0.024 (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: 2.654 (sec). Leaf size: 2649

DSolve[x^2*D[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],x,IncludeSingularSolutions -> True]
 

Too large to display