76.14.3 problem 31

Internal problem ID [17641]
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 : 31
Date solved : Tuesday, January 28, 2025 at 10:46:35 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 37

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

\[ y = \frac {a \cos \left (\frac {\sqrt {k}\, x}{\sqrt {m}}\right ) \sqrt {k}+b \sqrt {m}\, \sin \left (\frac {\sqrt {k}\, x}{\sqrt {m}}\right )}{\sqrt {k}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 46

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

\[ y(x)\to a \cos \left (\frac {\sqrt {k} x}{\sqrt {m}}\right )+\frac {b \sqrt {m} \sin \left (\frac {\sqrt {k} x}{\sqrt {m}}\right )}{\sqrt {k}} \]