second derivatives

Question

Using the second order derivative equation: ( (d²y)/(dx²) )-9y=o

 

Which of the following would be true?

 

y= e^3x

 

y=e^-3x

 

y=2e^-3x

 

y=xe^3x

 

Answer 1

you can find the second derivative in each case and then plug it in the given equation to check if it is satisfied.

 

just by seeing the first one ,we can see that double der of e³^x  is 9 e^3x.

 

since y is e^3x  we can see that first equation is satisfied. you can check for the others.second is definitely not true.plz check for the other 2