85.27.9 problem 9

Internal problem ID [22601]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 9
Date solved : Thursday, October 02, 2025 at 08:54:53 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y+y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 3, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 16

ode=D[y[x],{x,2}]+4*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin (2 x)+3 \cos (2 x) \end{align*}

✓ Sympy. Time used: 0.032 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sin {\left (2 x \right )} + 3 \cos {\left (2 x \right )} \]