88.23.6 problem 7
Internal
problem
ID
[24180]
Book
:
Elementary
Differential
Equations.
By
Lee
Roy
Wilcox
and
Herbert
J.
Curtis.
1961
first
edition.
International
texbook
company.
Scranton,
Penn.
USA.
CAT
number
61-15976
Section
:
Chapter
5.
Special
Techniques
for
Linear
Equations.
Miscellaneous
Exercises
at
page
162
Problem
number
:
7
Date
solved
:
Thursday, October 02, 2025 at 10:00:32 PM
CAS
classification
:
[[_high_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\left (10\right )}+y&=x^{10} \end{align*}
✓ Maple. Time used: 0.064 (sec). Leaf size: 165
ode:=diff(diff(diff(diff(diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x),x),x),x),x)+y(x) = x^10;
dsolve(ode,y(x), singsol=all);
\[
y = \left (c_3 \cos \left (\frac {\left (\sqrt {5}+1\right ) x}{4}\right )+c_4 \sin \left (\frac {\left (\sqrt {5}+1\right ) x}{4}\right )\right ) {\mathrm e}^{-\frac {\sqrt {10-2 \sqrt {5}}\, x}{4}}+\left (c_5 \cos \left (\frac {\left (\sqrt {5}+1\right ) x}{4}\right )+c_6 \sin \left (\frac {\left (\sqrt {5}+1\right ) x}{4}\right )\right ) {\mathrm e}^{\frac {\sqrt {10-2 \sqrt {5}}\, x}{4}}+\left (c_7 \cos \left (\frac {\left (\sqrt {5}-1\right ) x}{4}\right )+c_8 \sin \left (\frac {\left (\sqrt {5}-1\right ) x}{4}\right )\right ) {\mathrm e}^{-\frac {\sqrt {10+2 \sqrt {5}}\, x}{4}}+\left (c_9 \cos \left (\frac {\left (\sqrt {5}-1\right ) x}{4}\right )+\textit {\_C10} \sin \left (\frac {\left (\sqrt {5}-1\right ) x}{4}\right )\right ) {\mathrm e}^{\frac {\sqrt {10+2 \sqrt {5}}\, x}{4}}+x^{10}+c_1 \cos \left (x \right )+c_2 \sin \left (x \right )-3628800
\]
✓ Mathematica. Time used: 0.007 (sec). Leaf size: 317
ode=D[y[x],{x,10}]+y[x]==x^10;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to x^{10}+c_3 \cos (x)+e^{-\frac {1}{2} \sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} x} \left (c_1 e^{\sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} x}+c_5\right ) \cos \left (\frac {1}{4} \left (\sqrt {5}-1\right ) x\right )+c_2 e^{\frac {1}{2} \sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} x} \cos \left (\frac {1}{4} \left (1+\sqrt {5}\right ) x\right )+c_4 e^{-\frac {1}{2} \sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} x} \cos \left (\frac {1}{4} \left (1+\sqrt {5}\right ) x\right )+c_8 \sin (x)+c_6 e^{-\frac {1}{2} \sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} x} \sin \left (\frac {1}{4} \left (\sqrt {5}-1\right ) x\right )+c_{10} e^{\frac {1}{2} \sqrt {\frac {1}{2} \left (5+\sqrt {5}\right )} x} \sin \left (\frac {1}{4} \left (\sqrt {5}-1\right ) x\right )+c_7 e^{-\frac {1}{2} \sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} x} \sin \left (\frac {1}{4} \left (1+\sqrt {5}\right ) x\right )+c_9 e^{\frac {1}{2} \sqrt {\frac {1}{2} \left (5-\sqrt {5}\right )} x} \sin \left (\frac {1}{4} \left (1+\sqrt {5}\right ) x\right )-3628800 \end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x**10 + y(x) + Derivative(y(x), (x, 10)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : Cannot find 10 solutions to the homogeneous equation necessary to apply undete