Question

number of value of m belong to n for which y=e to the power mx is soln.of y'''-3y"-4y'+12y=0
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Answer 1

Answer:

It's similar to yours Question solutions

Step-by-step explanation:

Let,

y=e

mx

thenD(y)=me

mx

,D

2

(y)=m

2

e

mx

,D

3

(y)=m

3

e

mx

then given

D

3

(y)−3D

2

(y)−4D(y)+12y=0

⇒m

3

e

mx

−3m

3

e

mx

−4me

mx

+12e

mx

=0

∴m

3

−3m

2

−4m+12=0(∵e

mx



=0)

⇒(m−2)(m−3)(m+2)=0

⇒m=2,3,−2

Hence, the number of values of m ∈ N will be 2.........(∵−2 does not belong to the set of natural numbers)