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#### nathancurtis11

##### New member

- Sep 3, 2013

- 10

Question 3:

Let f : (0, +∞) → (all real) be a 2-times diﬀerentiable function. Deﬁne g: (all real) → (all real) by setting g(t) = f(e

^{t}).

a) why is g 2-times differentiable

b) Compute the derivatives f′ and f′′ by means of g' and g′′

c). Prove that f is a solution of the diﬀerential equation x

^{2}y′′+3xy′+y=x if and only if g is a solution of second order diﬀerential equation to determine.