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 : Monday, January 27, 2025 at 09:21:20 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*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

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

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

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