8.7.3 problem 3

Internal problem ID [809]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 11:51:59 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = 8; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 4 \sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+4*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 4 \sin (2 x)+3 \cos (2 x) \]

✓ Sympy. Time used: 0.063 (sec). Leaf size: 15

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): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 \sin {\left (2 x \right )} + 3 \cos {\left (2 x \right )} \]