85.66.5 problem 6 (b)

Internal problem ID [22891]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 213
Problem number : 6 (b)
Date solved : Thursday, October 02, 2025 at 09:16:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=x^4*diff(diff(y(x),x),x)+2*x^3*diff(y(x),x)+y(x) = 1/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (\frac {1}{x}\right ) c_2 +\cos \left (\frac {1}{x}\right ) c_1 +\frac {-2 x^{2}+1}{x^{2}} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 25

ode=x^4*D[y[x],{x,2}]+2*x^3*D[y[x],x]+y[x]==1/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{x^2}+c_1 \cos \left (\frac {1}{x}\right )-c_2 \sin \left (\frac {1}{x}\right )-2 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4*Derivative(y(x), (x, 2)) + 2*x**3*Derivative(y(x), x) + y(x) - 1/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**6*Derivative(y(x), (x, 2)) - x**2*y(x