54.3.160 problem 1174

Internal problem ID [12455]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1174
Date solved : Wednesday, October 01, 2025 at 01:45:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 25

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-x^5*ln(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{5} \ln \left (x \right )}{12}-\frac {7 x^{5}}{144}+c_1 \,x^{2}+c_2 x \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 32

ode=-(x^5*Log[x]) + 2*y[x] - 2*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 {7 x^5}{144}+\frac {1}{12} x^5 \log (x)+c_2 x^2+c_1 x \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5*log(x) + x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} x + \frac {x^{4} \log {\left (x \right )}}{12} - \frac {7 x^{4}}{144}\right ) \]