29.9.22 problem 262

Internal problem ID [4862]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 262
Date solved : Sunday, March 30, 2025 at 04:05:22 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 53

ode:=x^2*diff(y(x),x)+x^2*a+b*x*y(x)+c*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x \left (\sqrt {4 a c -b^{2}-2 b -1}\, \tan \left (\frac {\sqrt {4 a c -b^{2}-2 b -1}\, \left (\ln \left (x \right )+c_1 \right )}{2}\right )+b +1\right )}{2 c} \]

✓ Mathematica. Time used: 60.163 (sec). Leaf size: 66

ode=x^2 D[y[x],x]+a x^2 +b x y[x]+c y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {x \left (-\sqrt {4 a c-b^2-2 b-1} \tan \left (\frac {1}{2} \sqrt {4 a c-b^2-2 b-1} (-\log (x)+c_1)\right )+b+1\right )}{2 c} \]

✗ Sympy

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

Timed Out