28.2.44 problem 44

Internal problem ID [4487]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 44
Date solved : Sunday, March 30, 2025 at 03:23:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.409 (sec). Leaf size: 38

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

\[ y(x)\to 2 x-e^x (x-c_2) \cos (x)+\frac {1}{2} (1+2 c_1) e^x \sin (x)+1 \]

✓ Sympy. Time used: 0.247 (sec). Leaf size: 22

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

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