81.11.26 problem 15-25

Internal problem ID [21650]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-25
Date solved : Thursday, October 02, 2025 at 07:59:27 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y&=4 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+diff(y(x),x)+6*y(x) = 4*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 \cos \left (2 x \right )}{65}+\frac {11 \sin \left (2 x \right )}{65}+c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{2 x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 46

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+D[y[x],x]+6*y[x]==4*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {11}{65} \sin (2 x)+\frac {3}{65} \cos (2 x)+c_1 e^{-x}+c_2 e^{2 x}+c_3 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.118 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 4*sin(2*x) + Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{2 x} + C_{3} e^{3 x} + \frac {11 \sin {\left (2 x \right )}}{65} + \frac {3 \cos {\left (2 x \right )}}{65} \]