43.5.4 problem 1(d)

Internal problem ID [8914]
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 : Tuesday, September 30, 2025 at 06:00:03 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*}

✓ Maple. Time used: 0.079 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+10*y(x) = 0; 
ic:=[y(0) = Pi, D(y)(0) = Pi^2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {\pi ^2 \sin \left (\sqrt {10} x\right )}{\sqrt {10}}+\pi \cos \left (\sqrt {10} x\right ) \end{align*}

✓ Sympy. Time used: 0.040 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): pi, Subs(Derivative(y(x), x), x, 0): pi**2} 
dsolve(ode,func=y(x),ics=ics)
 

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