44.13.19 problem 18

Internal problem ID [9320]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 06:16:23 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \\ y^{\prime }\left (0\right )&=4 \\ y^{\prime \prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 18

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

\[ y = -\frac {{\mathrm e}^{-x}}{2}+\frac {9 \,{\mathrm e}^{x}}{2}-x \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to -x-\frac {e^{-x}}{2}+\frac {9 e^x}{2} \end{align*}

✓ Sympy. Time used: 0.103 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = - x + \frac {9 e^{x}}{2} - \frac {e^{- x}}{2} \]