74.1.42 problem 49

Internal problem ID [15751]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 49
Date solved : Monday, March 31, 2025 at 01:47:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-12*y(x) = 0; 
ic:=y(0) = 1, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {2 \,{\mathrm e}^{4 x}}{7}+\frac {5 \,{\mathrm e}^{-3 x}}{7} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 23

ode=D[y[x],{x,2}]-D[y[x],x]-12*y[x]==0; 
ic={y[0]==1,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{7} e^{-3 x} \left (2 e^{7 x}+5\right ) \]

✓ Sympy. Time used: 0.187 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {2 e^{4 x}}{7} + \frac {5 e^{- 3 x}}{7} \]