15.23.11 problem 15
Internal
problem
ID
[3361]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
41,
page
195
Problem
number
:
15
Date
solved
:
Monday, January 27, 2025 at 07:34:53 AM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries]]
\begin{align*} 4 x^{2} y^{\prime \prime }-3 \left (x^{2}+x \right ) y^{\prime }+2 y&=0 \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 435
Order:=6;
dsolve(4*x^2*diff(y(x),x$2)-3*(x+x^2)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[
y \left (x \right ) = x^{{7}/{8}} \left (c_{2} x^{\frac {\sqrt {17}}{8}} \left (1+\frac {21+3 \sqrt {17}}{8 \sqrt {17}+32} x +\frac {9}{128} \frac {\left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right )} x^{2}+\frac {9}{1024} \frac {\left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right )} x^{3}+\frac {27}{32768} \frac {\left (31+\sqrt {17}\right ) \left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right ) \left (16+\sqrt {17}\right )} x^{4}+\frac {81}{1310720} \frac {\left (39+\sqrt {17}\right ) \left (31+\sqrt {17}\right ) \left (23+\sqrt {17}\right ) \left (15+\sqrt {17}\right ) \left (7+\sqrt {17}\right )}{\left (4+\sqrt {17}\right ) \left (8+\sqrt {17}\right ) \left (12+\sqrt {17}\right ) \left (16+\sqrt {17}\right ) \left (20+\sqrt {17}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} x^{-\frac {\sqrt {17}}{8}} \left (1+\frac {-21+3 \sqrt {17}}{8 \sqrt {17}-32} x +\frac {9}{128} \frac {\left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right )} x^{2}+\frac {9}{1024} \frac {\left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right )} x^{3}+\frac {27}{32768} \frac {\left (-31+\sqrt {17}\right ) \left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right ) \left (-16+\sqrt {17}\right )} x^{4}+\frac {81}{1310720} \frac {\left (-39+\sqrt {17}\right ) \left (-31+\sqrt {17}\right ) \left (-23+\sqrt {17}\right ) \left (-15+\sqrt {17}\right ) \left (-7+\sqrt {17}\right )}{\left (-4+\sqrt {17}\right ) \left (-8+\sqrt {17}\right ) \left (-12+\sqrt {17}\right ) \left (-16+\sqrt {17}\right ) \left (-20+\sqrt {17}\right )} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 2028
AsymptoticDSolveValue[4*x^2*D[y[x],{x,2}]-3*(x+x^2)*D[y[x],x]+2*y[x]==0,y[x],{x,0,"6"-1}]
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