76.13.36 problem 36

Internal problem ID [17618]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 10:45:38 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: 0.042 (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)
 

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

✓ Solution by Mathematica

Time used: 0.009 (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]
 

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