Internal problem ID [6911]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
Order:=8; dsolve((1+9*x^2)*diff(y(x),x$2)-18*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (9 x^{2}+1\right ) y \left (0\right )+\left (x +3 x^{3}-\frac {27}{5} x^{5}+\frac {729}{35} x^{7}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[(1+9*x^2)*y''[x]-18*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (9 x^2+1\right )+c_2 \left (\frac {729 x^7}{35}-\frac {27 x^5}{5}+3 x^3+x\right ) \]