Internal problem ID [11907]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 6, Series solutions of linear differential equations. Section 6.2 (Frobenius).
Exercises page 251
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 x^{2} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}-3\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
Order:=6; dsolve(2*x^2*diff(y(x),x$2)+x*diff(y(x),x)+(2*x^2-3)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {5}{2}} \left (1-\frac {1}{9} x^{2}+\frac {1}{234} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1+x^{2}-\frac {1}{6} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 46
AsymptoticDSolveValue[2*x^2*y''[x]+x*y'[x]+(2*x^2-3)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_2 \left (-\frac {x^4}{6}+x^2+1\right )}{x}+c_1 \left (\frac {x^4}{234}-\frac {x^2}{9}+1\right ) x^{3/2} \]