ENGR 2422 Engineering Mathematics 2

Appendix to Chapter 3

General Checklist for First Order ODEs

 

P dx  +  Q dy  =  0

 

 

Test in the order

§       separable

§       linear

§       exact

§       integrating factor as a function of  x only

§       integrating factor as a function of  y only

 

 

If  P  and  Q  can both be written in the form 

(a function of  x only) ´ (a function of  y only)

then the ODE is separable.

Rewrite in the form    and solve.

 

If not:

 

Can the ODE be written in the form

y' + P(x)y = R(x) ?

If so, it is linear:

         and             

 

If not:

 

Is   Py  =  Qx ?

If so, then the ODE is exact.

Find , etc.

 

If not:

 

Is  R  =  (Py - Qx)/Q  a function of  x only?

If so, the integrating factor is

Then , etc.

 

If not:

Is  R  =  (Qx - Py)/P  a function of  y only?

If so, the integrating factor is 

Then , etc.


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Created 2001 03 01 and modified 2001 03 01 by Dr. G.H. George