76.14.1 problem 29

Internal problem ID [17639]
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 4.4 (Mechanical and electrical vibration). Problems at page 250
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 10:46:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+2*y(x)=0,y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = \sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 19

DSolve[{D[y[x],{x,2}]+2*y[x]==0,{y[0]==0,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2} \sin \left (\sqrt {2} x\right ) \]