9.15.5 problem 5

Internal problem ID [3209]
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 : 5
Date solved : Tuesday, September 30, 2025 at 06:28:20 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 42

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

\[ y = \frac {x^{6}}{360}+\frac {x^{4}}{12}-\frac {x^{5}}{60}+\frac {c_2 \,x^{3}}{6}+\frac {c_3 \,x^{2}}{2}+{\mathrm e}^{-x} c_1 +c_4 x +c_5 \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 53

ode=D[y[x],{x,5}]+D[y[x],{x,4}]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^6}{360}-\frac {x^5}{60}+\frac {x^4}{12}+c_5 x^3+c_4 x^2+c_3 x+c_1 e^{-x}+c_2 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} e^{- x} + \frac {x^{6}}{360} - \frac {x^{5}}{60} + \frac {x^{4}}{12} \]