12.19.55 problem section 9.3, problem 55

Internal problem ID [2202]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 55
Date solved : Tuesday, March 04, 2025 at 01:51:39 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+11 y^{\prime \prime }-14 y^{\prime }+10 y&=-{\mathrm e}^{x} \left (\sin \left (x \right )+2 \cos \left (2 x \right )\right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 44

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+11*diff(diff(y(x),x),x)-14*diff(y(x),x)+10*y(x) = -exp(x)*(sin(x)+2*cos(2*x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x} \left (\left (6 c_3 +\frac {7}{3}\right ) \cos \left (2 x \right )+\left (x +6 c_4 \right ) \sin \left (2 x \right )+\left (x +6 c_1 \right ) \cos \left (x \right )+6 \left (c_2 +\frac {1}{9}\right ) \sin \left (x \right )\right )}{6} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 53

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+11*D[y[x],{x,2}]-14*D[y[x],x]+10*y[x]==-Exp[x]*(Sin[x]+2*Cos[2*x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{36} e^x ((11+36 c_2) \cos (2 x)+(1+36 c_3) \sin (x)+6 \cos (x) (x+2 (x+6 c_1) \sin (x)+6 c_4)) \]

✓ Sympy. Time used: 0.581 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((sin(x) + 2*cos(2*x))*exp(x) + 10*y(x) - 14*Derivative(y(x), x) + 11*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{3} \sin {\left (x \right )} + C_{4} \cos {\left (2 x \right )} + \left (C_{1} + \frac {x}{6}\right ) \sin {\left (2 x \right )} + \left (C_{2} + \frac {x}{6}\right ) \cos {\left (x \right )}\right ) e^{x} \]