DifferentialOrder - Maple Help

Home : Support : Online Help : Education : Student Packages : ODEs : DifferentialOrder

Student[ODEs]

 DifferentialOrder
 find the differential order of an ODE

 Calling Sequence DifferentialOrder(expr) DifferentialOrder(expr, x) DifferentialOrder(expr, y(x))

Parameters

 expr - an expression x - name; the independent variable y - name; the dependent variable

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\right):$
 > $\mathrm{ode1}≔\mathrm{diff}\left(y\left(t\right),t,t\right)+\left(z\left(t\right)+1\right)+{z\left(t\right)}^{2}\left(t-1\right)\mathrm{diff}\left(z\left(t\right),t\right)=\mathrm{diff}\left(f\left(x\right),x,x,x\right)$
 ${\mathrm{ode1}}{≔}\frac{{{ⅆ}}^{{2}}}{{ⅆ}{{t}}^{{2}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({t}\right){+}{z}{}\left({t}\right){+}{1}{+}{{z}{}\left({t}\right)}^{{2}}{}\left({t}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{z}{}\left({t}\right)\right){=}\frac{{{ⅆ}}^{{3}}}{{ⅆ}{{x}}^{{3}}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{f}{}\left({x}\right)$ (1)
 > $\mathrm{DifferentialOrder}\left(\mathrm{ode1}\right)$
 ${3}$ (2)
 > $\mathrm{DifferentialOrder}\left(\mathrm{ode1},t\right)$
 ${2}$ (3)
 > $\mathrm{DifferentialOrder}\left(\mathrm{ode1},z\left(t\right)\right)$
 ${1}$ (4)

Compatibility

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