84.3.8 problem 2.8

Internal problem ID [22085]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 2. Solutions. Solved problems page 5
Problem number : 2.8
Date solved : Thursday, October 02, 2025 at 08:23:42 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 )&=1 \\ y \left (\frac {\pi }{2}\right )&=2 \\ \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+4*y(x) = 0; 
ic:=[y(0) = 1, y(1/2*Pi) = 2]; 
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]==1,y[Pi/2] ==2}; 
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): 1, y(pi/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions