20.8.11 problem Problem 11

Internal problem ID [3744]
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 11
Date solved : Monday, January 27, 2025 at 07:57:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+16 y&=34 \,{\mathrm e}^{x}+16 \cos \left (4 x \right )-8 \sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(diff(y(x),x$2)+16*y(x)=34*exp(x)+16*cos(4*x)-8*sin(4*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.636 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+16*y[x]==34*Exp[x]+16*Cos[4*x]-8*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 e^x+\left (x+\frac {1}{4}+c_1\right ) \cos (4 x)+\left (2 x-\frac {1}{8}+c_2\right ) \sin (4 x) \]