54.1.161 problem 164

Internal problem ID [11475]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 164
Date solved : Tuesday, September 30, 2025 at 08:31:15 PM
CAS classification : [_rational, _Riccati]

\begin{align*} 2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 a^{2} x&=0 \end{align*}

✓ Maple. Time used: 0.023 (sec). Leaf size: 102

ode:=2*x^2*diff(y(x),x)-2*y(x)^2-3*x*y(x)+2*a^2*x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-2 x c_1 \sqrt {-\frac {a^{2}}{x}}-x \right ) \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right )-x \left (c_1 -2 \sqrt {-\frac {a^{2}}{x}}\right ) \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right )}{2 \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right ) c_1 +2 \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right )} \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 94

ode=2*x^2*D[y[x],x]- 2*y[x]^2 - 3*x*y[x] + 2*a^2*x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {4 a^2 c_1 \sqrt {x}+2 a \sqrt {x} e^{\frac {4 a}{\sqrt {x}}}-x e^{\frac {4 a}{\sqrt {x}}}+2 a c_1 x}{2 e^{\frac {4 a}{\sqrt {x}}}-4 a c_1}\\ y(x)&\to a \left (-\sqrt {x}\right )-\frac {x}{2} \end{align*}

✗ 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) - 3*x*y(x) - 2*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

RecursionError : maximum recursion depth exceeded