Internal problem ID [636]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{3}\right ) = 2, y^{\prime }\left (\frac {\pi }{3}\right ) = -4\right ] \end {align*}
✓ Solution by Maple
Time used: 0.027 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+y(x) = 0,y(1/3*Pi) = 2, D(y)(1/3*Pi) = -4],y(x), singsol=all)
\[ y \relax (x ) = \left (\sin \relax (x )+2 \cos \relax (x )\right ) \sqrt {3}+\cos \relax (x )-2 \sin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[{y''[x]+y[x]==0,{y[Pi/3]==2,y'[Pi/3]==-4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\sqrt {3}-2\right ) \sin (x)+\left (1+2 \sqrt {3}\right ) \cos (x) \\ \end{align*}