75.4.2 problem 2

Internal problem ID [19941]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter IV. Ordinary linear differential equations with constant coefficients. Exercises at page 48
Problem number : 2
Date solved : Thursday, October 02, 2025 at 05:04:21 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

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

\[ y = \left (c_1 \,{\mathrm e}^{2 x \sqrt {3}}+c_2 \right ) {\mathrm e}^{-\left (1+\sqrt {3}\right ) x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to e^{-\left (\left (1+\sqrt {3}\right ) x\right )} \left (c_2 e^{2 \sqrt {3} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{x \left (-1 + \sqrt {3}\right )} + C_{2} e^{- x \left (1 + \sqrt {3}\right )} \]