74.1.45 problem 52

Internal problem ID [15825]
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 : 52
Date solved : Tuesday, January 28, 2025 at 08:08:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 18

dsolve([diff(y(x),x$3)-4*diff(y(x),x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = 0],y(x), singsol=all)
 

\[ y = 1-\frac {{\mathrm e}^{2 x}}{4}+\frac {{\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

DSolve[{D[y[x],{x,3}]-4*D[y[x],x]==0,{y[0]==1,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (e^{-2 x}-e^{2 x}+4\right ) \]