55.2.62 problem 62

Internal problem ID [13288]
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 : 62
Date solved : Wednesday, October 01, 2025 at 05:50:51 AM
CAS classification : [_rational, _Riccati]

\begin{align*} \left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime }&=y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0} \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 6861

ode:=(a__2*x^2+b__2*x+c__2)*diff(y(x),x) = y(x)^2+(a__1*x+b__1)*y(x)+a__0*x^2+b__0*x+c__0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=(a2*x^2+b2*x+c2)*D[y[x],x]==y[x]^2+(a1*x+b1)*y[x]+a0*x^2+b0*x+c0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a__0 = symbols("a__0") 
a__1 = symbols("a__1") 
a__2 = symbols("a__2") 
b__0 = symbols("b__0") 
b__1 = symbols("b__1") 
b__2 = symbols("b__2") 
c__0 = symbols("c__0") 
c__2 = symbols("c__2") 
y = Function("y") 
ode = Eq(-a__0*x**2 - b__0*x - c__0 - (a__1*x + b__1)*y(x) + (a__2*x**2 + b__2*x + c__2)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out