28.2.58 problem 58

Internal problem ID [4501]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 58
Date solved : Monday, January 27, 2025 at 09:21:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{-x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=sin(exp(-x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==Sin[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
 

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