34.11.4 problem 29

Internal problem ID [8025]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 05:14:23 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=\sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

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

\[ y = \frac {\sin \left (2 x \right )}{15}+c_1 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 90

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

\begin{align*} y(x)&\to e^x \int _1^x\frac {1}{4} e^{-K[1]} \sin (2 K[1])dK[1]+e^{-x} \int _1^x-\frac {1}{4} e^{K[2]} \sin (2 K[2])dK[2]+c_1 e^x+c_3 e^{-x}+\frac {1}{3} \sin (x) \cos (x)+c_2 \cos (x)+c_4 \sin (x) \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} + C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (x \right )} + \frac {\sin {\left (2 x \right )}}{15} \]