33.4.1 problem Problem 12.9

Internal problem ID [7822]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. Supplementary Problems. page 109
Problem number : Problem 12.9
Date solved : Tuesday, September 30, 2025 at 05:05:59 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{x^{5}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+y(x) = exp(x)/x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_2 +c_1 x +\frac {1}{12 x^{3}}\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \frac {1}{12} e^x \left (\frac {1}{x^3}+12 c_2 x+12 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x + \frac {1}{12 x^{3}}\right ) e^{x} \]