67.15.81 problem 22.15 (h)

Internal problem ID [16799]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (h)
Date solved : Thursday, October 02, 2025 at 01:39:04 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=64 x^{2} \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = 64*x^2*ln(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 29

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==64*x^2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-2 x^4+2 \left (2 x^4+c_2\right ) \log (x)+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.204 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-64*x**2*log(x) + x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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