23.3.21 problem 21

Internal problem ID [5735]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 21
Date solved : Tuesday, September 30, 2025 at 02:02:16 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} -2 y+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=-2*y(x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\sqrt {2}\, x}+c_2 \,{\mathrm e}^{-\sqrt {2}\, x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 31

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

\begin{align*} y(x)&\to c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x} \end{align*}

✓ Sympy. Time used: 0.041 (sec). Leaf size: 22

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

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