85.27.2 problem 2

Internal problem ID [22594]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 60
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:54:49 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\prime \prime \prime \prime }&=\frac {x}{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(diff(diff(diff(y(x),x),x),x),x) = 1/3*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{360} x^{5}+\frac {1}{6} c_1 \,x^{3}+\frac {9}{2} c_1^{2} x +\frac {1}{2} c_2 \,x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 31

ode=D[y[x],{x,4}]==x/3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^5}{360}+c_4 x^3+c_3 x^2+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.042 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x/3 + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + \frac {x^{5}}{360} \]