60.1.160 problem 163

Internal problem ID [10174]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 163
Date solved : Sunday, March 30, 2025 at 03:21:37 PM
CAS classification : [_rational, _Riccati]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

\[ y = \sqrt {x}\, a \tanh \left (\frac {i c_1 \sqrt {x}+2 a}{\sqrt {x}}\right ) \]

✓ Mathematica. Time used: 0.444 (sec). Leaf size: 43

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

\[ y(x)\to -\sqrt {-a^2} \sqrt {x} \tan \left (\frac {2 \sqrt {-a^2}}{\sqrt {x}}-c_1\right ) \]

✗ Sympy

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

RecursionError : maximum recursion depth exceeded