74.13.23 problem 40

Internal problem ID [16310]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 40
Date solved : Thursday, March 13, 2025 at 08:10:16 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 9

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

\[ y = 2 t +1 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 10

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

\[ y(t)\to 2 t+1 \]

✓ Sympy. Time used: 0.082 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = 2 t + 1 \]