88.17.2 problem 6

Internal problem ID [24113]
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 127
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:59:20 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+y&=\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 71

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+y(x) = sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_4 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}}+2 c_2 \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}}\right ) \sin \left (\frac {\sqrt {2}\, x}{2}\right )}{2}+c_3 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+c_1 \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+\frac {\sin \left (x \right )}{2} \]

✓ Mathematica. Time used: 0.362 (sec). Leaf size: 80

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

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

✓ Sympy. Time used: 0.114 (sec). Leaf size: 75

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

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