75.19.13 problem 630

Internal problem ID [17050]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 630
Date solved : Thursday, March 13, 2025 at 09:11:52 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=-\frac {16 \ln \left (x \right )}{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)-3*y(x) = -16*ln(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 c_{2} x^{4}+8 \ln \left (x \right )^{2}+4 \ln \left (x \right )+4 c_{1} +1}{4 x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 35

ode=x^2*D[y[x],{x,2}]-x*D[y[x],x]-3*y[x]==-16*Log[x]/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {4 c_2 x^4+8 \log ^2(x)+4 \log (x)+1+4 c_1}{4 x} \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) - 3*y(x) + 16*log(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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