Internal problem ID [4545]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+16 y-16 \cos \left (4 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (x ) = \cos \left (4 x \right )+2 x \sin \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 17
DSolve[{y''[x]+16*y[x]==16*Cos[4*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 x \sin (4 x)+\cos (4 x) \\ \end{align*}