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Differential Equations: Second Order (Auxiliary Equation with 2 Different Real Roots)

The

general

solution to

d2p dx2

– 11

dp dx

– 26 p = 0

is

=

e

+ e

Worked Solution:

The differential equation is second order, homogeneous and has constant coefficients.
We can therefore use the auxiliary equation: ² – 11 – 26 = 0
It factorises: ( + 2) ( – 13) = 0

The two roots of the auxiliary equation are

–2

and

13

The general solution is

p = A e ^{– 2 x} + B e^{13 x} where A and B are arbitrary constants.

© MEI Produced by Dr Ron Knott, 5 April 2007

Test reference: DEorder2a.html?ref=99403