true or false?

Question

y=e^-x satisfies the differential equation, ( (d²y)/(dt²) )+y=0

 

true or false?

Answer 1

it should be y=e^-t.   Little typo there, but no worries.

 

 

This is a second order differential equation.  We can write this as

 

y'' + y = 0

 

 

if y=e^-t , then

 

y' = -e^-t

 

y'' = e^-t

 

 

Plugging the values into the equation

 

e^-t+ e^-t = 0

 

2e^-t ≠ 0

 

 

The equation is not satisfied.