This routine is used to return an equivalent list form for a given linear ordinary differential equation.  The list returned has two elements.

The first is a list (here called A) of the coefficients of the ODE, of the form

The second element is the right hand side of the given ODE.  In the case that the DE has no right hand side, the default zero is used.

In the event that convertAlg cannot isolate for the proper list form (for instance, if the DE is not a linear ODE) then FAIL is returned.

This function is part of the DEtools package, and so it can be used in the form convertAlg(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[convertAlg](..).

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

$A≔\mathrm{diff}\left(y\left(x\right)\,x\right)\sin \left(x\right)-x\cos \left(x\right)\mathrm{diff}\left(y\left(x\right)\,x\,x\right)+\mathrm{diff}\left(y\left(x\right)\,x\right)-\tan \left(x\right)y\left(x\right)=5$

$A≔\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)\sin \left(x\right)-x\cos \left(x\right)\left(\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)\right)+\frac{\ⅆ}{\ⅆx}y\left(x\right)-\tan \left(x\right)y\left(x\right)=5$

$\mathrm{convertAlg}\left(A\,y\left(x\right)\right)$

$\left[\left[-\tan \left(x\right)\,\sin \left(x\right)+1\,-x\cos \left(x\right)\right]\,5\right]$

$B≔\mathrm{D}\left(y\right)\left(x\right)x\cdot 5-{\mathrm{D}}^{\left(2\right)}\left(y\right)\left(x\right)\sin \left(x\right)+{\mathrm{D}}^{\left(2\right)}\left(y\right)\left(x\right)x{3}^2$

$B≔5\mathrm{D}\left(y\right)\left(x\right)x-{\mathrm{D}}^{\left(2\right)}\left(y\right)\left(x\right)\sin \left(x\right)+9{\mathrm{D}}^{\left(2\right)}\left(y\right)\left(x\right)x$

$\mathrm{convertAlg}\left(B\,y\left(x\right)\right)$

$\left[\left[0\,5x\,-\sin \left(x\right)+9x\right]\,0\right]$