28.2.25 problem 25

Internal problem ID [4468]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 25
Date solved : Tuesday, March 04, 2025 at 06:46:05 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x) = 9*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\sqrt {3}\, {\mathrm e}^{\sqrt {3}\, x} c_{2}}{3}-\frac {\sqrt {3}\, {\mathrm e}^{-\sqrt {3}\, x} c_{1}}{3}-x^{3}-2 x +c_3 \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 52

ode=D[y[x],{x,3}]-3*D[y[x],x]==9*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -x^3-2 x+\frac {c_1 e^{\sqrt {3} x}}{\sqrt {3}}-\frac {c_2 e^{-\sqrt {3} x}}{\sqrt {3}}+c_3 \]

✓ Sympy. Time used: 0.190 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**2 - 3*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- \sqrt {3} x} + C_{3} e^{\sqrt {3} x} - x^{3} - 2 x \]