85.36.2 problem 1 (b)

Internal problem ID [22730]
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 171
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 09:14:08 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+y&=\sin \left (x \right )+{\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 1607

ode:=3*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)+y(x) = exp(-x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 1.155 (sec). Leaf size: 1634

ode=3*D[y[x],{x,4}]-5*D[y[x],{x,3}]+y[x]==Exp[-x]+Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - sin(x) - 5*Derivative(y(x), (x, 3)) + 3*Derivative(y(x), (x, 4)) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Cannot find 4 solutions to the homogeneous equation necessary to apply undeter