28.2.18 problem 18

Internal problem ID [4461]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 18
Date solved : Sunday, March 30, 2025 at 03:23:13 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

\[ y = \frac {\left (-x^{2}-4 c_2 +2\right ) \cos \left (x \right )}{4}+\frac {\left (4 c_1 +x \right ) \sin \left (x \right )}{4}+c_3 \]

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 36

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

\[ y(x)\to -\frac {1}{8} \left (2 x^2-3+8 c_2\right ) \cos (x)+\left (\frac {x}{4}+c_1\right ) \sin (x)+c_3 \]

✓ Sympy. Time used: 0.238 (sec). Leaf size: 22

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

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