88.20.5 problem 5
Internal
problem
ID
[24143]
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.
Exercises
at
page
146
Problem
number
:
5
Date
solved
:
Thursday, October 02, 2025 at 10:00:11 PM
CAS
classification
:
[[_high_order, _linear, _nonhomogeneous]]
\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }-y&=4 x^{5}-6 x^{2}+2 \end{align*}
✓ Maple. Time used: 0.007 (sec). Leaf size: 501
ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x)-y(x) = 4*x^5-6*x^2+2;
dsolve(ode,y(x), singsol=all);
\[
y = -4 x^{5}+6 x^{2}-480 x -2+c_1 \,{\mathrm e}^{\frac {\sqrt {3 \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{2}/{3}}-6 \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+12}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{24}}+c_2 \,{\mathrm e}^{-\frac {\sqrt {3 \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{2}/{3}}-6 \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+12}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{24}}+c_3 \,{\mathrm e}^{\frac {\sqrt {2}\, \sqrt {3}\, \sqrt {\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+2}\, \sqrt {i \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \sqrt {3}-2 i \sqrt {3}-\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}-2}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{48}}+c_4 \,{\mathrm e}^{-\frac {\sqrt {2}\, \sqrt {3}\, \sqrt {\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+2}\, \sqrt {i \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \sqrt {3}-2 i \sqrt {3}-\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}-2}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{48}}+c_5 \,{\mathrm e}^{\frac {\sqrt {2}\, \sqrt {3}\, \sqrt {\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+2}\, \sqrt {-i \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \sqrt {3}+2 i \sqrt {3}-\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}-2}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{48}}+c_6 \,{\mathrm e}^{-\frac {\sqrt {2}\, \sqrt {3}\, \sqrt {\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}+2}\, \sqrt {-i \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \sqrt {3}+2 i \sqrt {3}-\left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}}-2}\, \left (100+12 \sqrt {3}\, \sqrt {23}\right )^{{1}/{3}} \left (-3 \sqrt {3}+\sqrt {23}\right ) x}{48}}
\]
✓ Mathematica. Time used: 0.006 (sec). Leaf size: 765
ode=D[y[x],{x,6}]+D[y[x],{x,4}]-y[x]==4*x^5-6*x^2+2;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✓ Sympy. Time used: 2.561 (sec). Leaf size: 1448
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-4*x**5 + 6*x**2 - y(x) + Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 6)) - 2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\text {Solution too large to show}
\]