52.2.1 problem 1
Internal
problem
ID
[8252]
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.
6.3
SOLUTIONS
ABOUT
SINGULAR
POINTS.
EXERCISES
6.3.
Page
255
Problem
number
:
1
Date
solved
:
Monday, January 27, 2025 at 03:47:04 PM
CAS
classification
:
[[_Emden, _Fowler]]
\begin{align*} x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y&=0 \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✗ Solution by Maple
Order:=8;
dsolve(x^3*diff(y(x),x$2)+4*x^2*diff(y(x),x)+3*y(x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.090 (sec). Leaf size: 374
AsymptoticDSolveValue[x^3*D[y[x],{x,2}]+4*x^2*D[y[x],x]+3*y[x]==0,y[x],{x,0,"8"-1}]
\[
y(x)\to \frac {c_1 e^{-\frac {2 i \sqrt {3}}{\sqrt {x}}} \left (-\frac {9447234753831875 i \sqrt {3} x^{13/2}}{4611686018427387904}+\frac {3806522094375 i \sqrt {3} x^{11/2}}{4503599627370496}-\frac {14315125825 i x^{9/2}}{8796093022208 \sqrt {3}}+\frac {8083075 i x^{7/2}}{4294967296 \sqrt {3}}-\frac {15015 i \sqrt {3} x^{5/2}}{8388608}+\frac {385 i \sqrt {3} x^{3/2}}{8192}+\frac {935276240629355625 x^7}{147573952589676412928}-\frac {625538464175625 x^6}{288230376151711744}+\frac {930483178625 x^5}{844424930131968}-\frac {509233725 x^4}{549755813888}+\frac {425425 x^3}{268435456}-\frac {5005 x^2}{524288}-\frac {315 x}{512}-\frac {35 i \sqrt {x}}{16 \sqrt {3}}+1\right )}{x^{5/4}}+\frac {c_2 e^{\frac {2 i \sqrt {3}}{\sqrt {x}}} \left (\frac {9447234753831875 i \sqrt {3} x^{13/2}}{4611686018427387904}-\frac {3806522094375 i \sqrt {3} x^{11/2}}{4503599627370496}+\frac {14315125825 i x^{9/2}}{8796093022208 \sqrt {3}}-\frac {8083075 i x^{7/2}}{4294967296 \sqrt {3}}+\frac {15015 i \sqrt {3} x^{5/2}}{8388608}-\frac {385 i \sqrt {3} x^{3/2}}{8192}+\frac {935276240629355625 x^7}{147573952589676412928}-\frac {625538464175625 x^6}{288230376151711744}+\frac {930483178625 x^5}{844424930131968}-\frac {509233725 x^4}{549755813888}+\frac {425425 x^3}{268435456}-\frac {5005 x^2}{524288}-\frac {315 x}{512}+\frac {35 i \sqrt {x}}{16 \sqrt {3}}+1\right )}{x^{5/4}}
\]