26.7.34 problem Exercise 20, problem 35, page 220

Internal problem ID [7084]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20, problem 35, page 220
Date solved : Tuesday, September 30, 2025 at 04:21:15 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime \prime }+5 y^{\prime \prime }+y^{\prime }-y&=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 )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 21

ode:=3*diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = 0; 
ic:=[y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (9 \,{\mathrm e}^{\frac {4 x}{3}}+4 x -9\right ) {\mathrm e}^{-x}}{16} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=3*D[y[x],{x,3}]+5*D[y[x],{x,2}]+D[y[x],x]-y[x]==0; 
ic={y[0]==0,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{16} e^{-x} \left (4 x+9 e^{4 x/3}-9\right ) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) + 3*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): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {x}{4} - \frac {9}{16}\right ) e^{- x} + \frac {9 e^{\frac {x}{3}}}{16} \]