87.16.6 problem 6

Internal problem ID [23575]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:43:05 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

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

\[ y = -\frac {x^{3}}{2}-\frac {3 x^{2}}{4}-\frac {3 x}{4}-\frac {15}{8}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {7}\, x}{2}\right )+c_3 \,{\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {7}\, x}{2}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 73

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

\begin{align*} y(x)&\to \frac {1}{8} \left (-4 x^3-6 x^2-6 x-15\right )+c_3 e^x+c_2 e^{-x/2} \cos \left (\frac {\sqrt {7} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {7} x}{2}\right ) \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 56

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

\[ y{\left (x \right )} = C_{3} e^{x} - \frac {x^{3}}{2} - \frac {3 x^{2}}{4} - \frac {3 x}{4} + \left (C_{1} \sin {\left (\frac {\sqrt {7} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {7} x}{2} \right )}\right ) e^{- \frac {x}{2}} - \frac {15}{8} \]