29.6.21 problem 167

Internal problem ID [4767]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 167
Date solved : Tuesday, March 04, 2025 at 07:14:30 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 24

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

\[ y \left (x \right ) = \frac {\tan \left (\sqrt {a b}\, \left (x +c_{1} \right )\right ) x \sqrt {a b}}{b} \]

✓ Mathematica. Time used: 19.208 (sec). Leaf size: 33

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

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

✗ 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