28.2.34 problem 34

Internal problem ID [4477]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 34
Date solved : Sunday, March 30, 2025 at 03:23:34 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 24

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 4*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-x +c_3 -1\right ) \sin \left (x \right )+\left (c_1 +x \right ) \cos \left (x \right )+c_2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 29

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

\[ y(x)\to c_3 e^x+(x+c_1) \cos (x)+(-x-1+c_2) \sin (x) \]

✓ Sympy. Time used: 0.205 (sec). Leaf size: 20

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

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