64.13.16 problem 16

Internal problem ID [13475]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 16
Date solved : Monday, March 31, 2025 at 07:58:58 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=4 \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = 4*ln(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==4*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1}{x^2}+2 \log (x)+\frac {c_2}{x}-3 \]

✓ Sympy. Time used: 0.221 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 4*x*Derivative(y(x), x) + 2*y(x) - 4*log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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