28.2.28 problem 28

Internal problem ID [4471]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 28
Date solved : Monday, January 27, 2025 at 09:19:11 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+16 y&=64 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 69

dsolve(diff(y(x),x$4)+16*y(x)=64*cos(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 82

DSolve[D[y[x],{x,4}]+16*y[x]==64*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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