Internal problem ID [633]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.3 Complex Roots of the Characteristic Equation ,
page 164
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)+ 4*y(x) = 0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (2 x \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 10
DSolve[{y''[x]+4*y[x]==0,{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x) \cos (x) \\ \end{align*}