54.3.152 problem 1166

Internal problem ID [12447]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1166
Date solved : Wednesday, October 01, 2025 at 01:45:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

\[ y = \frac {x \left (4 \ln \left (x \right ) c_1 +3 x^{2}+4 c_2 \right )}{4} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 23

ode=-3*x^3 + y[x] - 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 {3 x^3}{4}+c_1 x+c_2 x \log (x) \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3 + x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} \log {\left (x \right )} + \frac {3 x^{2}}{4}\right ) \]