52.1.28 problem 25 expansion at 1
Internal
problem
ID
[8245]
Book
:
DIFFERENTIAL
EQUATIONS
with
Boundary
Value
Problems.
DENNIS
G.
ZILL,
WARREN
S.
WRIGHT,
MICHAEL
R.
CULLEN.
Brooks/Cole.
Boston,
MA.
2013.
8th
edition.
Section
:
CHAPTER
6
SERIES
SOLUTIONS
OF
LINEAR
EQUATIONS.
Section
6.2
SOLUTIONS
ABOUT
ORDINARY
POINTS.
EXERCISES
6.2.
Page
246
Problem
number
:
25
expansion
at
1
Date
solved
:
Sunday, March 30, 2025 at 12:49:36 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} \cos \left (x \right ) y^{\prime \prime }+y^{\prime }+5 y&=0 \end{align*}
Using series method with expansion around
\begin{align*} 1 \end{align*}
✓ Maple. Time used: 0.027 (sec). Leaf size: 497
Order:=8;
ode:=cos(x)*diff(diff(y(x),x),x)+diff(y(x),x)+5*y(x) = 0;
dsolve(ode,y(x),type='series',x=1);
\[
\text {Expression too large to display}
\]
✓ Mathematica. Time used: 0.008 (sec). Leaf size: 1808
ode=Cos[x]*D[y[x],{x,2}]+D[y[x],x]+5*y[x]==0;
ic={};
AsymptoticDSolveValue[{ode,ic},y[x],{x,1,7}]
Too large to display
✓ Sympy. Time used: 2.223 (sec). Leaf size: 299
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(5*y(x) + cos(x)*Derivative(y(x), (x, 2)) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_ordinary",x0=1,n=8)
\[
y{\left (x \right )} = C_{2} \left (x - \frac {5 \left (x - 1\right )^{6}}{48 \cos ^{3}{\left (x + 1 \right )}} + \frac {\left (x - 1\right )^{6}}{36 \cos ^{4}{\left (x + 1 \right )}} - \frac {\left (x - 1\right )^{6}}{720 \cos ^{5}{\left (x + 1 \right )}} + \frac {5 \left (x - 1\right )^{5}}{24 \cos ^{2}{\left (x + 1 \right )}} - \frac {\left (x - 1\right )^{5}}{8 \cos ^{3}{\left (x + 1 \right )}} + \frac {\left (x - 1\right )^{5}}{120 \cos ^{4}{\left (x + 1 \right )}} + \frac {5 \left (x - 1\right )^{4}}{12 \cos ^{2}{\left (x + 1 \right )}} - \frac {\left (x - 1\right )^{4}}{24 \cos ^{3}{\left (x + 1 \right )}} - \frac {5 \left (x - 1\right )^{3}}{6 \cos {\left (x + 1 \right )}} + \frac {\left (x - 1\right )^{3}}{6 \cos ^{2}{\left (x + 1 \right )}} - \frac {\left (x - 1\right )^{2}}{2 \cos {\left (x + 1 \right )}} - 1\right ) + C_{1} \left (- \frac {25 \left (x - 1\right )^{6}}{144 \cos ^{3}{\left (x + 1 \right )}} + \frac {5 \left (x - 1\right )^{6}}{48 \cos ^{4}{\left (x + 1 \right )}} - \frac {\left (x - 1\right )^{6}}{144 \cos ^{5}{\left (x + 1 \right )}} - \frac {5 \left (x - 1\right )^{5}}{12 \cos ^{3}{\left (x + 1 \right )}} + \frac {\left (x - 1\right )^{5}}{24 \cos ^{4}{\left (x + 1 \right )}} + \frac {25 \left (x - 1\right )^{4}}{24 \cos ^{2}{\left (x + 1 \right )}} - \frac {5 \left (x - 1\right )^{4}}{24 \cos ^{3}{\left (x + 1 \right )}} + \frac {5 \left (x - 1\right )^{3}}{6 \cos ^{2}{\left (x + 1 \right )}} - \frac {5 \left (x - 1\right )^{2}}{2 \cos {\left (x + 1 \right )}} + 1\right ) + O\left (x^{8}\right )
\]