Internal problem ID [9651]
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: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {\left (c_{2} x^{2}+b_{2} x +a_{2}\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (x b_{1}+a_{1}\right ) y+a_{0}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 18039
dsolve((c__2*x^2+b__2*x+a__2)*(diff(y(x),x)+lambda*y(x)^2)+(b__1*x+a__1)*y(x)+a__0=0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 15.366 (sec). Leaf size: 1986
DSolve[(c2*x^2+b2*x+a2)*(y'[x]+\[Lambda]*y[x]^2)+(b1*x+a1)*y[x]+a0==0,y[x],x,IncludeSingularSolutions -> True]
Too large to display