88.19.3 problem 3

Internal problem ID [24131]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 139
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:00:05 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

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

\[ y = \frac {\left (2 c_1 x +x^{2}-4 c_1 +2 c_2 -4 x +6\right ) {\mathrm e}^{x}}{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.054 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to e^x \left (\frac {x^2}{2}+(-2+c_2) x+3+c_1-2 c_2\right )+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 20

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

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