Internal problem ID [13611]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 17. Second order Homogeneous equations with constant coefficients. Additional
exercises page 334
Problem number: 17.6 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+16 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 12] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+16*y(x)=0,y(0) = 4, D(y)(0) = 12],y(x), singsol=all)
\[ y \left (x \right ) = 3 \sin \left (4 x \right )+4 \cos \left (4 x \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[{y''[x]+16*y[x]==0,{y[0]==4,y'[0]==12}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 \sin (4 x)+4 \cos (4 x) \]