84.19.1 problem 12.1

Internal problem ID [22209]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 12. Second order linear homogeneous differential equations with constant coefficients. Solved problems. Page 64
Problem number : 12.1
Date solved : Thursday, October 02, 2025 at 08:36:15 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=D[y[x],{x,2}]-D[y[x],{x,1}]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.083 (sec). Leaf size: 14

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

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