15.15.8 problem 9

Internal problem ID [3212]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 9
Date solved : Sunday, March 30, 2025 at 01:21:20 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = sin(x)*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\sin \left (x \right )+\frac {x \cos \left (x \right )}{2}+{\mathrm e}^{x} c_1 -{\mathrm e}^{-x} c_2 +c_3 \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 34

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

\[ y(x)\to -\sin (x)+\frac {1}{2} x \cos (x)+c_1 e^x-c_2 e^{-x}+c_3 \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 24

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

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