2.14.2.21 problem 121 out of 2993

Link to actual problem [1202] \[ \boxed {x^{2} \left (3 x +1\right ) y^{\prime \prime }+x \left (x^{2}+12 x +2\right ) y^{\prime }+2 x \left (x +3\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).

type detected by program

{"second order series method. Regular singular point. Difference is integer"}

type detected by Maple

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}

\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= {\mathrm e}^{-\frac {x}{3}-\ln \left (x \right )-\frac {8 \ln \left (1+3 x \right )}{9}}\right ] \\ \left [R &= x, S \left (R \right ) &= x \left (1+3 x \right )^{\frac {8}{9}} {\mathrm e}^{\frac {x}{3}} y\right ] \\ \end{align*}