20.8.1 problem Problem 1

Internal problem ID [3734]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 1
Date solved : Monday, January 27, 2025 at 07:56:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-16 y&=20 \cos \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-16*y(x)=20*cos(4*x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} {\mathrm e}^{4 x}+c_{1} {\mathrm e}^{-4 x}-\frac {5 \cos \left (4 x \right )}{8} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]-16*y[x]==20*Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {5}{8} \cos (4 x)+c_1 e^{4 x}+c_2 e^{-4 x} \]