38.2.43 problem 43

Internal problem ID [8261]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 43
Date solved : Tuesday, September 30, 2025 at 05:20:46 PM
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 )&=0 \\ y^{\prime }\left (\pi \right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 8

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 9

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

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

✓ Sympy. Time used: 0.036 (sec). Leaf size: 7

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

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