Internal problem ID [4843]
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. 6.3.1 page
250
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Bessel]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+y^{\prime }+\left (x -\frac {4}{x}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.022 (sec). Leaf size: 47
Order:=6; dsolve(diff(x*diff(y(x),x),x)+(x-4/x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1-\frac {1}{12} x^{2}+\frac {1}{384} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (9 x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-144-36 x^{2}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 52
AsymptoticDSolveValue[D[x*D[y[x],x],x]+(x-4/x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {\left (x^2+8\right )^2}{64 x^2}-\frac {1}{16} x^2 \log (x)\right )+c_2 \left (\frac {x^6}{384}-\frac {x^4}{12}+x^2\right ) \]