Internal problem ID [11916]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
\[ \boxed {x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 32
Order:=6; dsolve(x*diff(y(x),x$2)-(x^2+2)*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{3} \left (1+\frac {1}{5} x^{2}+\frac {1}{35} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (12+6 x^{2}+\frac {3}{2} x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 44
AsymptoticDSolveValue[x*y''[x]-(x^2+2)*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^4}{8}+\frac {x^2}{2}+1\right )+c_2 \left (\frac {x^7}{35}+\frac {x^5}{5}+x^3\right ) \]