38.2.39 problem 39

Internal problem ID [8257]
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 : 39
Date solved : Tuesday, September 30, 2025 at 05:20:40 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 (\frac {\pi }{4}\right )&=3 \\ \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 0, D(y)(1/4*Pi) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

{}

✗ Sympy

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/4): 3} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions