Internal problem ID [5495]
Book: Advanced Mathematical 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=3/2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x^2+(3/2)^2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{-\frac {3 i}{2}} \left (1+\left (-\frac {1}{13}-\frac {3 i}{26}\right ) x^{2}+\left (-\frac {1}{2600}+\frac {9 i}{1300}\right ) x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{\frac {3 i}{2}} \left (1+\left (-\frac {1}{13}+\frac {3 i}{26}\right ) x^{2}+\left (-\frac {1}{2600}-\frac {9 i}{1300}\right ) x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 66
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(x^2+9/4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \left (-\frac {1}{2600}-\frac {9 i}{1300}\right ) c_1 x^{\frac {3 i}{2}} \left (x^4-(16+12 i) x^2-(8-144 i)\right )-\left (\frac {1}{2600}-\frac {9 i}{1300}\right ) c_2 x^{-\frac {3 i}{2}} \left (x^4-(16-12 i) x^2-(8+144 i)\right ) \]