54.3.291 problem 1308

Internal problem ID [12586]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1308
Date solved : Wednesday, October 01, 2025 at 02:10:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+x y-\ln \left (x \right )^{3}&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 40

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

\[ y = \frac {2 \ln \left (x \right )^{3}+6 \ln \left (x \right )^{2}+\left (8 c_1 \,x^{2}+9\right ) \ln \left (x \right )+8 c_2 \,x^{2}+6}{8 x} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 41

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

\begin{align*} y(x)&\to \frac {2 \log ^3(x)+6 \log ^2(x)+9 \log (x)+6}{8 x}+c_1 x+c_2 x \log (x) \end{align*}

✓ Sympy. Time used: 0.231 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = \frac {8 x^{2} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) + 2 \log {\left (x \right )}^{3} + 6 \log {\left (x \right )}^{2} + 9 \log {\left (x \right )} + 6}{8 x} \]