76.14.2 problem 30

Internal problem ID [17640]
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 : 30
Date solved : Tuesday, January 28, 2025 at 10:46:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{4}+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: 0.049 (sec). Leaf size: 20

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

\[ y = \frac {16 \sqrt {127}\, {\mathrm e}^{-\frac {x}{8}} \sin \left (\frac {\sqrt {127}\, x}{8}\right )}{127} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 30

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

\[ y(x)\to \frac {16 e^{-x/8} \sin \left (\frac {\sqrt {127} x}{8}\right )}{\sqrt {127}} \]