74.1.45 problem 52

Internal problem ID [15746]
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 : Thursday, March 13, 2025 at 06:17:13 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*}

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

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(y(x),x) = 0; 
ic:=y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.196 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): -1, Subs(Derivative(y(x), (x, 2)), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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