10.8.14 problem 20

Internal problem ID [1286]
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
Date solved : Monday, January 27, 2025 at 04:49:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{3}\right )&=2\\ y^{\prime }\left (\frac {\pi }{3}\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 22

dsolve([diff(y(x),x$2)+y(x) = 0,y(1/3*Pi) = 2, D(y)(1/3*Pi) = -4],y(x), singsol=all)
 

\[ y = \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \sqrt {3}+\cos \left (x \right )-2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 28

DSolve[{D[y[x],{x,2}]+y[x]==0,{y[Pi/3]==2,Derivative[1][y][ Pi/3 ]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (\sqrt {3}-2\right ) \sin (x)+\left (1+2 \sqrt {3}\right ) \cos (x) \]