Question

Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy/dx =-2. What is f(x)?

Answer 1

You have a differential equation here with an initial value.
All you have to do is evaluate the indefinite integral of:
\[\int\limits_{}^{} dy = \int\limits_{}^{} -2 ~~dx\]
Then evaluate when x = 0, y = 3, to find the Constant.
Plug the constant back into the equation for y, thus giving you your particular solution.

Answer 2

Make sense?..

Answer 3

\[\frac{ dy }{ dx } = - 2\]
\[dy = -2~~dx\]
\[\int\limits_{}^{} dy = \int\limits_{}^{} -2~~dx\]
and so on.

Answer 4

we havent done integrations yet so i dont know how to do those

Answer 5

is it
y = - 2x ?

Answer 6

?

Answer 7

yes.

Answer 8

y = -2x + C

Answer 9

input x = 0, y = 3 and solve for C now.
then plug C back in for the particular solution.

Answer 10

whats c ?

Answer 11

a constant.

Answer 12

then c is 3 right ?

Answer 13

correct.
so you have
y = -2x + 3

Answer 14

Just sketch that now, pretty simple stuff.

Answer 15

oh thanks

Answer 16

its a straight line but they asked for curve ?

Answer 17

does that matter ?

Answer 18

no it doesn't matter.. that is the curve..

Answer 19

oh ok thanks