35.9.10 problem 5, using elementary method

Internal problem ID [6245]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 5, using elementary method
Date solved : Wednesday, March 05, 2025 at 12:27:22 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

ode:=diff(diff(y(x),x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

ode=D[y[x],{x,2}]==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^x+c_2 e^{-x} \]

✓ Sympy. Time used: 0.058 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} \]