85.68.1 problem 1

Internal problem ID [22912]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 217
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:16:32 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&=64 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 33

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+4*diff(y(x),x)-8*y(x) = 64*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 +4 x -1\right ) \cos \left (2 x \right )+\left (-4 x +c_3 -3\right ) \sin \left (2 x \right )+c_2 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 37

ode=D[y[x],{x,3}]-2*D[y[x],{x,2}]+4*D[y[x],x]-8*y[x]==64*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_3 e^{2 x}+(4 x+c_1) \cos (2 x)+(-4 x-2+c_2) \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.194 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*y(x) - 64*sin(2*x) + 4*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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