When called with the single argument expr, DifferentialOrder(expr) returns the differential order of the highest derivative found in expr.

When called with a second argument x which is a name, DifferentialOrder(expr, x) returns the differential order of the highest derivative of a function with respect to the variable x that is found in expr.

Finally, when called with a second argument y(x) which is a function of a single argument, DifferentialOrder(expr, y(x)) returns the differential order of the highest derivative of y(x) with respect to x that is found in expr.

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

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

$\mathrm{ode1}≔\frac{{\ⅆ}^2}{\ⅆt^2}y\left(t\right)+z\left(t\right)+1+{z\left(t\right)}^2\left(t-1\right)\left(\frac{\ⅆ}{\ⅆt}z\left(t\right)\right)=\frac{{\ⅆ}^3}{\ⅆx^3}f\left(x\right)$

$\mathrm{DifferentialOrder}\left(\mathrm{ode1}\right)$

$3$

$\mathrm{DifferentialOrder}\left(\mathrm{ode1}\,t\right)$

$2$

$\mathrm{DifferentialOrder}\left(\mathrm{ode1}\,z\left(t\right)\right)$

$1$

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

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