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

The

general

solution to

4

d2y dx2

– 19

dy dx

– 30 y = 0

is

=

e

+ e

Worked Solution:

The differential equation is second order, homogeneous and has constant coefficients.
We can therefore use the auxiliary equation: 4 ² – 19 – 30 = 0
It factorises: ( – 6) (4 + 5) = 0

The two roots of the auxiliary equation are

6

and

–  5 4

The general solution is

y = A e^{6 x} + B e ^{– 5/4 x} where A and B are arbitrary constants.

© MEI Produced by Dr Ron Knott, 5 April 2007

Test reference: DEorder2a.html?ref=47165,qu=gen