60.3.169 problem 1183

Internal problem ID [11165]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1183
Date solved : Sunday, March 30, 2025 at 07:44:41 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-5*y(x)-x^2*ln(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{5}+\frac {c_1}{x}-\frac {x^{2} \ln \left (x \right )}{9} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 27

ode=-(x^2*Log[x]) - 5*y[x] - 3*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x^5-\frac {1}{9} x^2 \log (x)+\frac {c_1}{x} \]

✓ Sympy. Time used: 0.297 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*log(x) + x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x^{5} - \frac {x^{2} \log {\left (x \right )}}{9} \]