# Question:how to move all derivatives to one side of equation?

## Question:how to move all derivatives to one side of equation?

Maple 2019

To help decide the type of ODE, I need a function which moves all derivatives to lhs and everything else to the rhs of the ODE. This way I can more easily analyze the ODE.

The ode will be only first order. Any term which contains  (y')^n, is to be moved to the lhs. Rest to rhs. Couple of examples will help illustrate the problem. This is done in code only, without looking at the screen. The dependent variable is always y and the independent variable is x.  So I need to turn the ODE to the form

G(y',y'^2,y'^3,.....,y'^n)  = F(x,y)

I can find all derivatives in the ODE using

`indets['flat'](ode,{`^`('identical'(diff(y(x),x)),'algebraic'),'identical'(diff(y(x),x))})`

But not sure how this will help me do what I want. isolate does not help, since it only takes one term at a time. Collect also did not help for same reason.  If the ODE contains only ONE derivative, then it is easy to do. But the question is about how to do it for ODE which contains more than y' term of different powers as the examples below show.

What methods to do this in Maple? I looked at DEtools but so far did not see anything.

Example 1

 > restart; ode:=3*diff(y(x),x)^2+diff(y(x),x)^3+sin(x)+y(x)=x*y(x)+x*diff(y(x),x);

 > indets['flat'](ode,{`^`('identical'(diff(y(x),x)),'algebraic'),'identical'(diff(y(x),x))})

 > ode_wanted:= 3*diff(y(x),x)^2+diff(y(x),x)^3-x*diff(y(x),x)=-sin(x)-y(x)+x*y(x)

Example 2

 > restart; ode:=3*diff(y(x),x)^2+diff(y(x),x)=x*diff(y(x),x)+5;

 > indets['flat'](ode,{`^`('identical'(diff(y(x),x)),'algebraic'),'identical'(diff(y(x),x))})

 > ode_wanted:= 3*diff(y(x),x)^2+diff(y(x),x)-x*diff(y(x),x)=5

 >