56.4.42 problem 39
Internal
problem
ID
[8931]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
4.0
Problem
number
:
39
Date
solved
:
Monday, January 27, 2025 at 05:20:14 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} 2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x -5\right ) y&=0 \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 277
Order:=6;
dsolve(2*x^2*diff(y(x), x, x) +x*diff(y(x), x) +(x-5)*y(x) = 0,y(x),type='series',x=0);
\[
y = x^{{1}/{4}} \left (c_{1} x^{-\frac {\sqrt {41}}{4}} \left (1+\frac {1}{-2+\sqrt {41}} x +\frac {1}{2} \frac {1}{\left (-2+\sqrt {41}\right ) \left (-4+\sqrt {41}\right )} x^{2}+\frac {1}{6} \frac {1}{\left (-2+\sqrt {41}\right ) \left (-4+\sqrt {41}\right ) \left (-6+\sqrt {41}\right )} x^{3}+\frac {1}{24} \frac {1}{\left (-2+\sqrt {41}\right ) \left (-4+\sqrt {41}\right ) \left (-6+\sqrt {41}\right ) \left (-8+\sqrt {41}\right )} x^{4}+\frac {1}{120} \frac {1}{\left (-2+\sqrt {41}\right ) \left (-4+\sqrt {41}\right ) \left (-6+\sqrt {41}\right ) \left (-8+\sqrt {41}\right ) \left (-10+\sqrt {41}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {\sqrt {41}}{4}} \left (1+\frac {1}{-2-\sqrt {41}} x +\frac {1}{2} \frac {1}{\left (2+\sqrt {41}\right ) \left (4+\sqrt {41}\right )} x^{2}-\frac {1}{6} \frac {1}{\left (2+\sqrt {41}\right ) \left (4+\sqrt {41}\right ) \left (6+\sqrt {41}\right )} x^{3}+\frac {1}{24} \frac {1}{\left (2+\sqrt {41}\right ) \left (4+\sqrt {41}\right ) \left (6+\sqrt {41}\right ) \left (8+\sqrt {41}\right )} x^{4}-\frac {1}{120} \frac {1}{\left (2+\sqrt {41}\right ) \left (4+\sqrt {41}\right ) \left (6+\sqrt {41}\right ) \left (8+\sqrt {41}\right ) \left (10+\sqrt {41}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 1668
AsymptoticDSolveValue[2*x^2*D[y[x],{x,2}]+x*D[y[x],x]+(x-5)*y[x]==0,y[x],{x,0,"6"-1}]
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