# Reducing and increase of order and ODE

1. Jul 30, 2015

### Bruno Tolentino

Two questions:

First: If is possible to reduce the order of an ODE increasing the number of equations, so, is possible do the inverse patch? In other words, is possible reduce the number of equations of a system of ODE increasing the order?

Second: This technique of reducing and increasing of order is applicable to a PDE/system of PDE?

2. Jul 30, 2015

### Staff: Mentor

3. Jul 30, 2015

### HallsofIvy

Staff Emeritus
Even in with linear equations, whether or not it is separable depends upon the geometry of the situation. An equation may be separable in one coordinate system and not in another.

4. Aug 1, 2015

### epenguin

You can certainly do that in the case where you did the opposite recently https://www.physicsforums.com/threads/system-of-ode-of-second-order.825408/ . More than one way around but if you differentiate one of the equations you will find you have enough to eliminate y and y' and finish with an 2nd order d.e. in x. Then with no added effort with one in y too. In general n linear d.e.s with constant coefficients like that you can get one n'th order one in one variable. In fact you can get n of them. But if you are interested in solutions you only need to get one, and the other solutions are merely a renaming of terms.

Last edited: Aug 2, 2015