55.2.45 problem 45

Internal problem ID [13271]
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 : 45
Date solved : Wednesday, October 01, 2025 at 04:59:01 AM
CAS classification : [_rational, _Riccati]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 827

ode:=(a__2*x+b__2)*(diff(y(x),x)+lambda*y(x)^2)+(a__1*x+b__1)*y(x)+a__0*x+b__0 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 4.28 (sec). Leaf size: 1432

ode=(a2*x+b2)*(D[y[x],x]+\[Lambda]*y[x]^2)+(a1*x+b1)*y[x]+a0*x+b0==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ 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") 
lambda_ = symbols("lambda_") 
y = Function("y") 
ode = Eq(a__0*x + b__0 + (a__1*x + b__1)*y(x) + (a__2*x + b__2)*(lambda_*y(x)**2 + Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out