23.5.138 problem 138

Internal problem ID [6747]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 138
Date solved : Tuesday, September 30, 2025 at 03:51:21 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=24 x \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 41

ode:=y(x)+2*diff(diff(y(x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = 24*sin(x)*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 c_4 x -6 x^{2}+2 c_1 +3\right ) \cos \left (x \right )}{2}-\left (x^{3}+\left (-c_3 -3\right ) x -c_2 \right ) \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 46

ode=y[x] + 2*D[y[x],{x,2}] + D[y[x],{x,4}] == 24*x*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (-2 x^3+(9+2 c_4) x+2 c_3\right ) \sin (x)+\left (-3 x^2+c_2 x+3+c_1\right ) \cos (x) \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*x*sin(x) + y(x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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