Second derivative of e^x minus e^x

In summary, the conversation discusses proving that y(t) = e^t is a solution of the equation y'' - y = 0 by substituting y=e^t and showing that y''-y=0.
  • #1
eagleswings
16
1

Homework Statement


Show that y(t) = e^t is a solution of y'' - y = 0,

Homework Equations


integral of e^x dx = e^x +c
derivative of e^x = e^x



The Attempt at a Solution


set m = d(e^t)/dt, which also = e^t then dm = e^t

then d(m)/dt = e^t if y(t) = e^t is a solution
integrate both sides m= e^t +c
substitute e^t = e^t + c which is true for C = 0
not sure if it is that simple
 
Physics news on Phys.org
  • #2
It's even more simple than that. Put y=e^t. y'=e^t. y''=e^t. y''-y=e^t-e^t=0. You don't need to say much more than that.
 
  • #3
Thanks Dick! sometimes it just helps to be able to ask someone else to look at it.
 

FAQ: Second derivative of e^x minus e^x

What is the second derivative of ex - ex?

The second derivative of ex - ex is 0.

Why is the second derivative of ex - ex equal to 0?

This is because the derivative of ex is ex and the derivative of a constant (in this case, ex) is 0. Therefore, when we take the derivative of ex - ex, we are essentially taking the derivative of 0, which results in 0.

What does the second derivative of ex - ex represent?

The second derivative represents the rate of change of the rate of change of the function ex - ex. In other words, it measures the curvature of the graph of the function.

How do you calculate the second derivative of ex - ex?

To calculate the second derivative, we can use the power rule. First, we take the derivative of ex, which is ex. Then, we take the derivative of ex again, which is also ex. Finally, we subtract the two derivatives to get 0.

What is the significance of the second derivative of ex - ex?

The second derivative of ex - ex is significant because it tells us about the curvature of the graph of the function. If the second derivative is positive, the graph is concave up, if it is negative, the graph is concave down, and if it is 0, the graph is a straight line. This information can be helpful in understanding the behavior of the function and making predictions about its values.

Back
Top