28.2.32 problem 32

Internal problem ID [4475]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 32
Date solved : Monday, January 27, 2025 at 09:20:30 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 27

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

\[ y \left (x \right ) = \left (-x +c_4 \right ) {\mathrm e}^{-x}+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_3 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 47

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

\[ y(x)\to c_2 \cos (x)+\frac {1}{2} e^{-x} \left (-2 x+2 c_1 e^{2 x}+2 c_4 e^x \sin (x)-3+2 c_3\right ) \]