23.1.183 problem 183

Internal problem ID [4790]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 183
Date solved : Tuesday, September 30, 2025 at 08:37:00 AM
CAS classification : [_rational, _Riccati]

\begin{align*} x y^{\prime }+a \,x^{2} y^{2}+2 y&=b \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 66

ode:=x*diff(y(x),x)+a*x^2*y(x)^2+2*y(x) = b; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\sqrt {-a b}\, \left (\operatorname {BesselY}\left (1, \sqrt {-a b}\, x \right ) c_1 +\operatorname {BesselJ}\left (1, \sqrt {-a b}\, x \right )\right )}{x a \left (c_1 \operatorname {BesselY}\left (0, \sqrt {-a b}\, x \right )+\operatorname {BesselJ}\left (0, \sqrt {-a b}\, x \right )\right )} \]

✓ Mathematica. Time used: 0.153 (sec). Leaf size: 158

ode=x*D[y[x],x]+a*x^2*y[x]^2+2*y[x]==b; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {i \sqrt {b} \left (\operatorname {BesselY}\left (1,-i \sqrt {a} \sqrt {b} x\right )-c_1 \operatorname {BesselJ}\left (1,i \sqrt {a} \sqrt {b} x\right )\right )}{\sqrt {a} x \left (\operatorname {BesselY}\left (0,-i \sqrt {a} \sqrt {b} x\right )+c_1 \operatorname {BesselJ}\left (0,i \sqrt {a} \sqrt {b} x\right )\right )}\\ y(x)&\to -\frac {i \sqrt {b} \operatorname {BesselJ}\left (1,i \sqrt {a} \sqrt {b} x\right )}{\sqrt {a} x \operatorname {BesselJ}\left (0,i \sqrt {a} \sqrt {b} x\right )} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(a*x**2*y(x)**2 - b + x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded