73.16.10 problem 24.1 (j)

Internal problem ID [15451]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (j)
Date solved : Monday, March 31, 2025 at 01:38:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (x^{2}+4 c_1 \right ) \ln \left (x \right )-x^{2}+4 c_2}{4 x^{2}} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 29

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.273 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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