Link to actual problem [1694] \[ \boxed {4 y t +\left (2 t^{2}+2 y\right ) y^{\prime }=-3 t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
type detected by program
{"exact", "differentialType"}
type detected by Maple
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{2 t^{2}+2 y}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {t^{3}+2 t^{2} y +y^{2}}{4 t^{2}+4 y}\right ] \\ \\ \end{align*}