Question

if dy/dx= 4e^4x -4, how do we find the coordinates of the stationary point?

Answer 1

first integrate it to find the relation between x and y
then use the given conditions to find the value of constant of integration

Answer 2

y=e^4x -4x which given conditions?

Answer 3

A stationary point is a point that's not moving right? So it's _change_ in position should be 0.

So set dy/dx=0 and solve for your coordinates!

Answer 4

i thought that with the derived equation we had to make that equal to 0 then solve for 'x', but when i solve for x i get 0 because 4e^4x -4=0 4e^4x=4 e^4x=1 4x=ln1 4x=0 therefore x=0

Answer 5

some conditions must be provided to solve this differential equation

Answer 6

maybe im doing something wrong, how do you solve 4e^4x -4=0 for 'x'?

Answer 7

You did. x=0.

But that's just where it is on the x-axis. You need a y-coordinate to determine where the point is.

Answer 8

thats what i thought too but the question doesnt give us a y coordinate. can we substitute x into y=e^4x -4x?
which is y=1 right?

Answer 9

Kind of... But remember, when you integrate you have a +C, so really the answer is y=1+C and until you determine what C is based on some extra conditions, you don't know.

But the best guess you can make is, (0,1+C) as the point.