45.2.6 problem 6
Internal
problem
ID
[7229]
Book
:
A
FIRST
COURSE
IN
DIFFERENTIAL
EQUATIONS
with
Modeling
Applications.
Dennis
G.
Zill.
9th
edition.
Brooks/Cole.
CA,
USA.
Section
:
Chapter
6.
SERIES
SOLUTIONS
OF
LINEAR
EQUATIONS.
Exercises.
6.2
page
239
Problem
number
:
6
Date
solved
:
Monday, January 27, 2025 at 02:48:33 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 351
Order:=6;
dsolve(x^2*(x-5)^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(x^2-25)*y(x)=0,y(x),type='series',x=0);
\[
y = x^{{21}/{50}} \left (c_{1} x^{-\frac {\sqrt {2941}}{50}} \left (1+\frac {-1166-4 \sqrt {2941}}{-3125+125 \sqrt {2941}} x -\frac {9}{15625} \frac {879 \sqrt {2941}-79709}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right )} x^{2}+\frac {\frac {15291084 \sqrt {2941}}{1953125}-\frac {906742764}{1953125}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right )} x^{3}-\frac {12}{244140625} \frac {-122814219551+2200649681 \sqrt {2941}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right ) \left (-100+\sqrt {2941}\right )} x^{4}+\frac {\frac {181292058002304 \sqrt {2941}}{152587890625}-\frac {10008934775328384}{152587890625}}{\left (-25+\sqrt {2941}\right ) \left (-50+\sqrt {2941}\right ) \left (-75+\sqrt {2941}\right ) \left (-100+\sqrt {2941}\right ) \left (-125+\sqrt {2941}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {\sqrt {2941}}{50}} \left (1+\frac {1166-4 \sqrt {2941}}{125 \sqrt {2941}+3125} x +\frac {\frac {7911 \sqrt {2941}}{15625}+\frac {717381}{15625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right )} x^{2}+\frac {\frac {15291084 \sqrt {2941}}{1953125}+\frac {906742764}{1953125}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right )} x^{3}+\frac {\frac {1473770634612}{244140625}+\frac {26407796172 \sqrt {2941}}{244140625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right ) \left (100+\sqrt {2941}\right )} x^{4}+\frac {\frac {181292058002304 \sqrt {2941}}{152587890625}+\frac {10008934775328384}{152587890625}}{\left (\sqrt {2941}+25\right ) \left (50+\sqrt {2941}\right ) \left (\sqrt {2941}+75\right ) \left (100+\sqrt {2941}\right ) \left (125+\sqrt {2941}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 5384
AsymptoticDSolveValue[x^2*(x-5)^2*D[y[x],{x,2}]+4*x*D[y[x],x]+(x^2-25)*y[x]==0,y[x],{x,0,"6"-1}]
Too large to display