# : 1. Consider the ordinary differential equation [8+8+8] dy dy dx? 2y = 0 dx (1) (a) Classify (linear or non linear) and state the

: 1. Consider the ordinary differential equation
[8+8+8]
dy dy
dx?
2y = 0
dx
(1)
(a) Classify (linear or non linear) and state the order of the above equation (1).
(b) Find the values of m such that the function f defined by f(x) = emx is a solution
of the differential equation (1).
(c) Show that for any choice of the constants c1 and c2, the function 6(x) = c1e¬ +
Cze2a is an explicit solution to the differential equation (1).

(550 words)

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