28.2.49 problem 49

Internal problem ID [4492]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 49
Date solved : Sunday, March 30, 2025 at 03:23:59 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = 10*exp(x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 34

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==10*Exp[x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (3 \sin (x)-\cos (x)+c_2 e^x+c_3 e^{2 x}+c_1\right ) \]

✓ Sympy. Time used: 0.288 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - 10*exp(x)*sin(x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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