Internal problem ID [13240]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.2 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([diff(y(x),x$2)+4*y(x)=0,y(0) = 2, D(y)(0) = 6],y(x), singsol=all)
\[ y = 3 \sin \left (2 x \right )+2 \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 18
DSolve[{y''[x]+4*y[x]==0,{y[0]==2,y'[0]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 \sin (2 x)+2 \cos (2 x) \]