Internal problem ID [14000]
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 (n).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 47
Order:=6; dsolve((9*x^2+9*x^3)*diff(y(x),x$2)+(9*x+27*x^2)*diff(y(x),x)+(8*x-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {\left (-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (x^{\frac {2}{3}} c_{2} +c_{1} \right )}{x^{\frac {1}{3}}}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 62
AsymptoticDSolveValue[(9*x^2+9*x^3)*y''[x]+(9*x+27*x^2)*y'[x]+(8*x-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (-x^5+x^4-x^3+x^2-x+1\right )+\frac {c_2 \left (-x^5+x^4-x^3+x^2-x+1\right )}{\sqrt [3]{x}} \]