28.2.48 problem 48

Internal problem ID [4491]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 48
Date solved : Sunday, March 30, 2025 at 03:23:58 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 2*exp(x)+5*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 28

ode=D[y[x],{x,3}]-D[y[x],{x,2}]+D[y[x],x]-y[x]==2*Exp[x]+5*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.180 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 5*exp(2*x) - 2*exp(x) + Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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