85.67.18 problem 18

Internal problem ID [22909]
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 216
Problem number : 18
Date solved : Thursday, October 02, 2025 at 09:16:31 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.941 (sec). Leaf size: 1536

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

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

✓ Mathematica. Time used: 0.252 (sec). Leaf size: 68

ode=D[y[x],{x,5}]-5*D[y[x],{x,3}]+4*D[y[x],x]==x^2-x+Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{72} \left (6 x^3-9 x^2+45 x-36 c_1 e^{-2 x}-72 c_2 e^{-x}+2 e^x (-6 x+5+36 c_3)+36 c_4 e^{2 x}+72 c_5\right ) \end{align*}

✓ Sympy. Time used: 0.217 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + x - exp(x) + 4*Derivative(y(x), x) - 5*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{3} e^{- 2 x} + C_{4} e^{- x} + C_{5} e^{2 x} + \frac {x^{3}}{12} - \frac {x^{2}}{8} + \frac {5 x}{8} + \left (C_{2} - \frac {x}{6}\right ) e^{x} \]