87.18.10 problem 10

Internal problem ID [23651]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:43:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 x}}{x^{4}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{2 x} \left (c_2 +c_1 x +\frac {1}{6 x^{2}}\right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {e^{2 x} \left (6 c_2 x^3+6 c_1 x^2+1\right )}{6 x^2} \end{align*}

✓ Sympy. Time used: 0.256 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x + \frac {1}{6 x^{2}}\right ) e^{2 x} \]