Values of Constant

[hgaon001]

the question reads... For certain values of the constant m the function f defined by f(x) = e^mx is a solution of the differential equation

(d^3y/dx^3)-3(d^2y/dx^2)-4(dy/dx)+12y=0

i got the 2nd and 3rd derivative.. then plugged in but i got to the point in which i got this

e^mx(m^3-3m^2-4m+12)

so then e^mx=0... but i dont know how to solve for (m^3-3m^2-4m+12) .. Please explain the process Thank u!

 

[Deleted member 4993]

the question reads... For certain values of the constant m the function f defined by f(x) = e^mx is a solution of the differential equation

(d^3y/dx^3)-3(d^2y/dx^2)-4(dy/dx)+12y=0

i got the 2nd and 3rd derivative.. then plugged in but i got to the point in which i got this

e^mx(m^3-3m^2-4m+12)

so then e^mx=0... but i dont know how to solve for (m^3-3m^2-4m+12) .. Please explain the process Thank u!

Did you study rational root theorem?

according to that theorem - the possible rational roots are 3,4,6,2,1,12.

Try those numbers to test for roots. After you find one - you will be left with a quadratic which can be solved by your favorite method.

 

[mmm4444bot]

I'm sure that Subhotosh intended to include the negative possibilities, too.

… according to that theorem - the possible rational roots are ±3, ±4, ±6, ±2, ±1, ±12 …

 

[Deleted member 4993]

Re:

I'm sure that Subhotosh intended to include the negative possibilities, too.

… according to that theorem - the possible rational roots are ±3, ±4, ±6, ±2, ±1, ±12 …

That was a very intelligent mistake on my part - thought about it - told myself to put those in text format - then promptly forgot it!!!!

 

[mmm4444bot]

… That was a very intelligent mistake …

Oh, good! This means that I must be very intelligent, too. :lol: