75.15.7 problem 438

Internal problem ID [16887]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 438
Date solved : Monday, March 31, 2025 at 03:34:45 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (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);
 

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

✓ Mathematica. Time used: 0.019 (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]
 

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

✓ Sympy. Time used: 0.174 (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)
 

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