Internal problem ID [13670]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional
Exercises. page 715
Problem number: 35.4 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x +10 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
Order:=6; dsolve((x^2-9*x^4)*diff(y(x),x$2)-6*x*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = c_{1} x^{5} \left (1+18 x^{2}+243 x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} x^{2} \left (12-108 x^{2}-2916 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 38
AsymptoticDSolveValue[(x^2-9*x^4)*y''[x]-6*x*y'[x]+10*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (243 x^9+18 x^7+x^5\right )+c_1 \left (-243 x^6-9 x^4+x^2\right ) \]