Internal problem ID [4741]
Book: Advanced Mathemtical Methods for Scientists and Engineers, Bender and Orszag. Springer
October 29, 1999
Section: Chapter 3. APPROXIMATE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS. page
136
Problem number: 3.25 v=1/2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 45
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2+(1/2)^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{-\frac {i}{2}} \left (1+\left (-\frac {1}{5}-\frac {i}{10}\right ) x^{2}+\left (\frac {7}{680}+\frac {3 i}{340}\right ) x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {i}{2}} \left (1+\left (-\frac {1}{5}+\frac {i}{10}\right ) x^{2}+\left (\frac {7}{680}-\frac {3 i}{340}\right ) x^{4}+\mathrm {O}\left (x^{6}\right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
AsymptoticDSolveValue[x^2*y''+x*y'[x]+(x^2+(1/2)^2)*y[x]==0,y[x],{x,0,5}]
Timed out