The Type(ODE, y(x)) returns a sequence of matching solvability types of ODE if any are found. Currently the only solvability types considered are: separable, linear, and exact.

The Type(ODE, class, y(x)) returns true or false indicating whether the ODE is of the given solvability type class.

The extra argument y(x) indicating the solving variable is optional in general, but it must be given when the solving variable cannot be determined unambiguously from the ODE.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\right)\:$

$\mathrm{types}≔\left[\mathrm{separable}\,\mathrm{linear}\,\mathrm{exact}\right]\:$

$\mathrm{ode1}≔x^2\left(y\left(x\right)+1\right)+{y\left(x\right)}^2\left(x-1\right)\mathrm{diff}\left(y\left(x\right)\,x\right)=0$

$\mathrm{ode1}≔x^2\left(y\left(x\right)+1\right)+{y\left(x\right)}^2\left(x-1\right)\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)=0$

$\mathrm{Type}\left(\mathrm{ode1}\,y\left(x\right)\right)$

$\left\{\mathrm{separable}\right\}$

$\mathrm{map2}\left(\mathrm{Type}\,\mathrm{ode1}\,\mathrm{types}\,y\left(x\right)\right)$

$\left[\mathrm{true}\,\mathrm{false}\,\mathrm{false}\right]$

$\mathrm{ode2}≔x^2\left(y\left(x\right)+1\right)+\left(x-1\right)+\mathrm{diff}\left(y\left(x\right)\,x\right)=0$

$\mathrm{ode2}≔x^2\left(y\left(x\right)+1\right)+x-1+\frac{\ⅆ}{\ⅆx}y\left(x\right)=0$

$\mathrm{Type}\left(\mathrm{ode2}\right)$

$\left\{\mathrm{linear}\right\}$

$\mathrm{map2}\left(\mathrm{Type}\,\mathrm{ode2}\,\mathrm{types}\right)$

$\left[\mathrm{false}\,\mathrm{true}\,\mathrm{false}\right]$

$\mathrm{ode3}≔\mathrm{diff}\left(x\left({y\left(x\right)}^2+1\right)+x^2\,x\right)=0$

$\mathrm{ode3}≔{y\left(x\right)}^2+1+2xy\left(x\right)\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)+2x=0$

$\mathrm{Type}\left(\mathrm{ode3}\right)$

$\left\{\mathrm{exact}\right\}$

$\mathrm{map2}\left(\mathrm{Type}\,\mathrm{ode3}\,\mathrm{types}\right)$

$\left[\mathrm{false}\,\mathrm{false}\,\mathrm{true}\right]$

$\mathrm{ode4}≔\mathrm{diff}\left(x\left(y\left(x\right)+1\right)\,x\right)=0$

$\mathrm{ode4}≔y\left(x\right)+1+x\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)=0$

$\mathrm{Type}\left(\mathrm{ode4}\right)$

$\left\{\mathrm{exact}\,\mathrm{linear}\,\mathrm{separable}\right\}$

$\mathrm{map2}\left(\mathrm{Type}\,\mathrm{ode4}\,\mathrm{types}\right)$

$\left[\mathrm{true}\,\mathrm{true}\,\mathrm{true}\right]$

The Student[ODEs][Type] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.