23.3.238 problem 240

Internal problem ID [5952]
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 : 240
Date solved : Tuesday, September 30, 2025 at 02:06:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} -y-2 y^{\prime }+4 y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=-y(x)-2*diff(y(x),x)+4*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {x \sqrt {5}}{2}}+c_2 \right ) {\mathrm e}^{-\frac {\left (\sqrt {5}-1\right ) x}{4}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to e^{-\frac {1}{4} \left (\sqrt {5}-1\right ) x} \left (c_2 e^{\frac {\sqrt {5} x}{2}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (1 - \sqrt {5}\right )}{4}} + C_{2} e^{\frac {x \left (1 + \sqrt {5}\right )}{4}} \]