Link to actual problem [8957] \[ \boxed {y^{\prime }-\frac {x^{2}}{y+x^{{3}/{2}}}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class C`]]
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 &= \frac {2 x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{{3}/{2}}}, S \left (R \right ) &= \frac {3 \ln \left (x \right )}{2}\right ] \\ \end{align*}
My program’s symgen result This shows my program’s found \(\xi ,\eta \) and the corresponding ODE in canonical coordinates \(R,S\).\begin{align*} \xi &= 0 \\ \eta &=\frac {3 x^{{3}/{2}} y -2 x^{3}+3 y^{2}}{2 x^{{3}/{2}}+2 y} \\ \frac {dS}{dR} &= 0 \\ \end{align*}