67.10.1 problem 15.2 (a)

Internal problem ID [16583]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (a)
Date solved : Thursday, October 02, 2025 at 01:36:36 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 )&=2 \\ y^{\prime }\left (0\right )&=6 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 2, D(y)(0) = 6]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 18

ode=D[y[x],{x,2}]+4*y[x]==0; 
ic={y[0]==2,Derivative[1][y][0] ==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.035 (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): 2, Subs(Derivative(y(x), x), x, 0): 6} 
dsolve(ode,func=y(x),ics=ics)
 

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