76.12.15 problem 26

Internal problem ID [17492]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.2 (Theory of second order linear homogeneous equations). Problems at page 226
Problem number : 26
Date solved : Thursday, March 13, 2025 at 10:10:30 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.004 (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);
 

\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{2} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.135 (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)
 

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