54.3.170 problem 1184

Internal problem ID [12465]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1184
Date solved : Wednesday, October 01, 2025 at 01:45:24 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 25

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x)-x^4+x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{2} \left (2 c_2 x +x^{2}+2 \ln \left (x \right )+2 c_1 +2\right )}{2} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 30

ode=x^2 - x^4 + 6*y[x] - 4*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} x^2 \left (x^2+2 \log (x)+2 c_2 x+2+2 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x**2*Derivative(y(x), (x, 2)) + x**2 - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} + C_{2} x + \frac {x^{2}}{2} + \log {\left (x \right )}\right ) \]