Internal problem ID [4315]
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.
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*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+16*y(x)=16*cos(4*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (4 x \right ) c_{2}+\cos \left (4 x \right ) c_{1}+\frac {\cos \left (4 x \right )}{2}+2 \sin \left (4 x \right ) x \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 28
DSolve[y''[x]+16*y[x]==16*Cos[4*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {1}{4}+c_1\right ) \cos (4 x)+(2 x+c_2) \sin (4 x) \\ \end{align*}