The DEdetermine command performs some sanity checks on the given ordinary differential equation and returns an LODEstruct data structure.

The first argument should be a differential equation in diff notation or in D operator notation. If ode is an expression, then it is equated to zero.

$\mathrm{with}\left(\mathrm{Slode}\right)\:$

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

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

$\mathrm{DEdetermine}\left(\mathrm{ode}\,y\left(x\right)\right)$

$\mathrm{LODEstruct}\left(\left\{\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)\left(x-1\right)-y\left(x\right)=0\right\}\,\left\{y\left(x\right)\right\}\right)$

$\mathrm{DEdetermine}\left(\mathrm{convert}\left(\mathrm{ode}\,\mathrm{D}\right)\,y\left(x\right)\right)$

$\mathrm{LODEstruct}\left(\left\{\mathrm{D}\left(y\right)\left(x\right)\left(x-1\right)-y\left(x\right)=0\right\}\,\left\{y\left(x\right)\right\}\right)$