Determining value

[kcoe05]

I am currently on my own for a differential equations math class and I am completely lost on a review problem in the book. I would greatly appreciate assistance for the following problem as it will help me prepare for my test.

Determine the value of M for which y=e^ mx is a solution of the differential equation: 2 (d^2y/dx^2) - 5(dy/dx) - 3y= 0

Thank you all so much for your help

 

[arthur ohlsten]

let y=e^mx
dy/dx= m e^mx
d^2y/dx^2= m^2e^mx

2d^2y/dx^2 - 5 dy/dx -3y=0
substitute
2m^2 e^mx -5 m e^mx -3 e^mx=0
e^mx { 2m^2 -5 m -3]=0
either e^mx=0 or [2m^2-5m -3]=0
e^mx=0 is trivial solution answer 1

2m^2-5m -3=0
[2m+1][m-3]=0
m=-1/2 or m=3 answer

Arthur

 

[kcoe05]

I think that one look a lot tougher than it really was! lol Thank you very much. You made it seem easier for me. Thanks!!!!