2.13.1.86 problem 86 out of 223

Link to actual problem [7097] \[ \boxed {t y^{\prime \prime }-y^{\prime }+4 t^{3} y=0} \]

type detected by program

{"kovacic", "second_order_bessel_ode", "second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_method_2"}

type detected by Maple

[[_Emden, _Fowler], [_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}^{i t \sqrt {t^{2}}}\right ] \\ \left [R &= t, S \left (R \right ) &= {\mathrm e}^{-i t \sqrt {t^{2}}} y\right ] \\ \end{align*}