Internal problem ID [9655]
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: 68.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {x^{2} \left (x +a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+\alpha x +\beta =0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 5852
dsolve(x^2*(x+a)*(diff(y(x),x)+lambda*y(x)^2)+x*(b*x+c)*y(x)+alpha*x+beta=0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 5.272 (sec). Leaf size: 2260
DSolve[x^2*(x+a)*(y'[x]+\[Lambda]*y[x]^2)+x*(b*x+c)*y[x]+\[Alpha]*x+\[Beta]==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display