Internal problem ID [6913]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises
page 355
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
Order:=8; dsolve((1+2*x^2)*diff(y(x),x$2)+11*x*diff(y(x),x)+9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {9}{2} x^{2}+\frac {105}{8} x^{4}-\frac {539}{16} x^{6}\right ) y \left (0\right )+\left (x -\frac {10}{3} x^{3}+9 x^{5}-\frac {156}{7} x^{7}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 54
AsymptoticDSolveValue[(1+2*x^2)*y''[x]+11*x*y'[x]+9*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (-\frac {156 x^7}{7}+9 x^5-\frac {10 x^3}{3}+x\right )+c_1 \left (-\frac {539 x^6}{16}+\frac {105 x^4}{8}-\frac {9 x^2}{2}+1\right ) \]