74.1.42 problem 49

Internal problem ID [15822]
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 : Tuesday, January 28, 2025 at 08:08:13 AM
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*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)-diff(y(x),x)-12*y(x)=0,y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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