74.1.44 problem 51

Internal problem ID [15753]
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 : 51
Date solved : Monday, March 31, 2025 at 01:47:10 PM
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 )&=0\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 15

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x) = 0; 
ic:=y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} \left (-2 x+3 e^{2 x}-3\right ) \]

✓ Sympy. Time used: 0.098 (sec). Leaf size: 17

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

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