35.6.17 problem 17

Internal problem ID [6167]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 17
Date solved : Monday, January 27, 2025 at 01:43:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 29

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

\[ y = \frac {\left (4 x +2 c_2 \right ) \sin \left (4 x \right )}{2}+\frac {\left (1+2 c_1 \right ) \cos \left (4 x \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 28

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

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