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:
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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