49.5.4 problem 1(d)

Internal problem ID [7628]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 59
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:08:03 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+10 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 27

dsolve([diff(y(x),x$2)+10*y(x)=0,y(0) = Pi, D(y)(0) = Pi^2],y(x), singsol=all)
 

\[ y = \frac {\pi \left (\pi \sqrt {10}\, \sin \left (\sqrt {10}\, x \right )+10 \cos \left (\sqrt {10}\, x \right )\right )}{10} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 33

DSolve[{D[y[x],{x,2}]+10*y[x]==0,{y[0]==Pi,Derivative[1][y][0] ==Pi^2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\pi ^2 \sin \left (\sqrt {10} x\right )}{\sqrt {10}}+\pi \cos \left (\sqrt {10} x\right ) \]