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Student[ODEs]

 Type
 classify the solvability type of a first order ODE, if possible

 Calling Sequence Type(ODE, y(x)) Type(ODE, class, y(x))

Parameters

 ODE - a first order ordinary differential equation y - name; the dependent variable x - name; the independent variable class - name; a solvability type

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\right):$
 > $\mathrm{types}≔\left[\mathrm{separable},\mathrm{linear},\mathrm{exact}\right]:$
 > $\mathrm{ode1}≔{x}^{2}\left(y\left(x\right)+1\right)+{y\left(x\right)}^{2}\left(x-1\right)\mathrm{diff}\left(y\left(x\right),x\right)=0$
 ${\mathrm{ode1}}{≔}{{x}}^{{2}}{}\left({y}{}\left({x}\right){+}{1}\right){+}{{y}{}\left({x}\right)}^{{2}}{}\left({x}{-}{1}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){=}{0}$ (1)
 > $\mathrm{Type}\left(\mathrm{ode1},y\left(x\right)\right)$
 $\left\{{\mathrm{separable}}\right\}$ (2)
 > $\mathrm{map2}\left(\mathrm{Type},\mathrm{ode1},\mathrm{types},y\left(x\right)\right)$
 $\left[{\mathrm{true}}{,}{\mathrm{false}}{,}{\mathrm{false}}\right]$ (3)
 > $\mathrm{ode2}≔{x}^{2}\left(y\left(x\right)+1\right)+\left(x-1\right)+\mathrm{diff}\left(y\left(x\right),x\right)=0$
 ${\mathrm{ode2}}{≔}{{x}}^{{2}}{}\left({y}{}\left({x}\right){+}{1}\right){+}{x}{-}{1}{+}\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right){=}{0}$ (4)
 > $\mathrm{Type}\left(\mathrm{ode2}\right)$
 $\left\{{\mathrm{linear}}\right\}$ (5)
 > $\mathrm{map2}\left(\mathrm{Type},\mathrm{ode2},\mathrm{types}\right)$
 $\left[{\mathrm{false}}{,}{\mathrm{true}}{,}{\mathrm{false}}\right]$ (6)
 > $\mathrm{ode3}≔\mathrm{diff}\left(x\left({y\left(x\right)}^{2}+1\right)+{x}^{2},x\right)=0$
 ${\mathrm{ode3}}{≔}{{y}{}\left({x}\right)}^{{2}}{+}{1}{+}{2}{}{x}{}{y}{}\left({x}\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){+}{2}{}{x}{=}{0}$ (7)
 > $\mathrm{Type}\left(\mathrm{ode3}\right)$
 $\left\{{\mathrm{exact}}\right\}$ (8)
 > $\mathrm{map2}\left(\mathrm{Type},\mathrm{ode3},\mathrm{types}\right)$
 $\left[{\mathrm{false}}{,}{\mathrm{false}}{,}{\mathrm{true}}\right]$ (9)
 > $\mathrm{ode4}≔\mathrm{diff}\left(x\left(y\left(x\right)+1\right),x\right)=0$
 ${\mathrm{ode4}}{≔}{y}{}\left({x}\right){+}{1}{+}{x}{}\left(\frac{{ⅆ}}{{ⅆ}{x}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{y}{}\left({x}\right)\right){=}{0}$ (10)
 > $\mathrm{Type}\left(\mathrm{ode4}\right)$
 $\left\{{\mathrm{exact}}{,}{\mathrm{linear}}{,}{\mathrm{separable}}\right\}$ (11)
 > $\mathrm{map2}\left(\mathrm{Type},\mathrm{ode4},\mathrm{types}\right)$
 $\left[{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}\right]$ (12)

Compatibility

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