15.25.9 problem 8
Internal
problem
ID
[3396]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
43,
page
209
Problem
number
:
8
Date
solved
:
Monday, January 27, 2025 at 07:35:39 AM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
\begin{align*} 9 x^{2} y^{\prime \prime }+\left (3 x +2\right ) y&=x^{4}+x^{2} \end{align*}
Using series method with expansion around
\begin{align*} 0 \end{align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 63
Order:=6;
dsolve(9*x^2*diff(y(x),x$2)+(2+3*x)*y(x)=x^2+x^4,y(x),type='series',x=0);
\[
y \left (x \right ) = c_{1} x^{{1}/{3}} \left (1-\frac {1}{2} x +\frac {1}{20} x^{2}-\frac {1}{480} x^{3}+\frac {1}{21120} x^{4}-\frac {1}{1478400} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{{2}/{3}} \left (1-\frac {1}{4} x +\frac {1}{56} x^{2}-\frac {1}{1680} x^{3}+\frac {1}{87360} x^{4}-\frac {1}{6988800} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+x^{2} \left (\frac {1}{20}-\frac {3}{1120} x +\frac {1129}{123200} x^{2}-\frac {3387}{22422400} x^{3}+\operatorname {O}\left (x^{4}\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.184 (sec). Leaf size: 264
AsymptoticDSolveValue[9*x^2*D[y[x],{x,2}]+(2+3*x)*y[x]==x^2+x^4,y[x],{x,0,"6"-1}]
\[
y(x)\to c_1 \sqrt [3]{x} \left (-\frac {x^5}{1478400}+\frac {x^4}{21120}-\frac {x^3}{480}+\frac {x^2}{20}-\frac {x}{2}+1\right )+x^{2/3} \left (-\frac {x^5}{6988800}+\frac {x^4}{87360}-\frac {x^3}{1680}+\frac {x^2}{56}-\frac {x}{4}+1\right ) \left (\frac {1057 x^{16/3}}{337920}-\frac {241 x^{13/3}}{6240}+\frac {21 x^{10/3}}{200}-\frac {x^{7/3}}{14}+\frac {x^{4/3}}{4}\right )+\sqrt [3]{x} \left (-\frac {x^5}{1478400}+\frac {x^4}{21120}-\frac {x^3}{480}+\frac {x^2}{20}-\frac {x}{2}+1\right ) \left (-\frac {223 x^{17/3}}{212160}+\frac {421 x^{14/3}}{23520}-\frac {57 x^{11/3}}{616}+\frac {x^{8/3}}{32}-\frac {x^{5/3}}{5}\right )+c_2 x^{2/3} \left (-\frac {x^5}{6988800}+\frac {x^4}{87360}-\frac {x^3}{1680}+\frac {x^2}{56}-\frac {x}{4}+1\right )
\]