37.1.9 problem 10.2.11 (iii)

Internal problem ID [6396]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page 307
Problem number : 10.2.11 (iii)
Date solved : Monday, January 27, 2025 at 02:00:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 16

dsolve([diff(y(x),x$2)+16*y(x)=16*cos(4*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
 

\[ y = \cos \left (4 x \right )+2 x \sin \left (4 x \right ) \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]+16*y[x]==16*Cos[4*x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x \sin (4 x)+\cos (4 x) \]