23.1.170 problem 170

Internal problem ID [4777]
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 : 170
Date solved : Tuesday, September 30, 2025 at 08:34:23 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 24

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

\[ y = \frac {\tan \left (\left (c_1 +x \right ) \sqrt {a b}\right ) x \sqrt {a b}}{b} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 30

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{b K[1]^2+a}dK[1]=x+c_1,y(x)\right ] \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded