85.64.5 problem 1 (e)

Internal problem ID [22872]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 1 (e)
Date solved : Thursday, October 02, 2025 at 09:16:00 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y&=x^{2}+16 \ln \left (x \right )^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+4*y(x) = x^2+16*ln(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{2}}+\frac {\ln \left (x \right ) c_1}{x^{2}}+4 \ln \left (x \right )^{2}+\frac {x^{2}}{16}-8 \ln \left (x \right )+6 \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 38

ode=x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+4*y[x]==x^2+16*(Log[x])^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2}{16}+\frac {c_1}{x^2}+\left (-8+\frac {2 c_2}{x^2}\right ) \log (x)+4 \log ^2(x)+6 \end{align*}

✓ Sympy. Time used: 0.224 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x**2 + 5*x*Derivative(y(x), x) + 4*y(x) - 16*log(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} \log {\left (x \right )} + \frac {x^{2} \left (x^{2} + 64 \log {\left (x \right )}^{2} - 128 \log {\left (x \right )} + 96\right )}{16}}{x^{2}} \]