Question

Differential equations? Calculus?

solve the differential equation.

f"(s) = sin x, f'(0)=1, f(0)=6

Answer 1

do you mean f"(x)?

Answer 2

yes sorry

Answer 3

Good morning, VBG!
Something seems not quite right here.
If f ' (x)=sin x and f ' (0), that appears to be two different definitions.
Am I correct in supposing you meant f '' (x) = sin x?

Answer 4

Assuming that It's f ' '(x) that equals sin x,
then f ' (x) = -cos x +C and f '(0) = 1 = -cos 0 + C. Make sense?

Answer 5

(laplace method is more fun)

Answer 6

Surely is. Vilbarguen is currently offline.

Answer 7

i hadn't thought of applying those initial conditions mid-way (so-to-speak) through solving, i usually wait till the end, but i see that will work fine and even make the method simpler

Answer 8

Hey guys. Sorry I had to leave. yes it is f '' (x), i just used " so I guess it looked like ' .

Answer 9

mathmale so f ' (x) = -cos x +C because it is the antiderivative yes?

Answer 10

Yes, i was confused there. But that's not your fault.

Integrate f ' ' (x) and add the constant of integration, C.
Find C, based upon the initial conditions.

Answer 11

Your f ' (x" is fine. Can you now find C? I know you must be working on that right now.

Answer 12

so if f ' (0)= 1, I use - cos (0) + C
= -1 + C
= -1 + 2
f'(0) = 1

Answer 13

am I right?

Answer 14

You are saying that C=2, right?

If so, then take your f '(x)=-cos x +2 and integrate every term with respect to x. Add another constant of integration, D.

Answer 15

hold on I don't understand. this is to solve f(0)=6 ?

Answer 16

VBG: You are to integrate your expression for f ' (x), adding a new constant, D, at the end.
Once you've done that, you take the last initial condition and insert those values into your f(x).

Here's what that would look like:

f(0)=6=-sin 0 +2(0) +D.

Find D.

then write

Answer 17

f(x) = ???? incorporating C=2 and D = ?
and then you're done.

Answer 18

f(0)= 6= -sin (0) + 2 (0) + D
= 0 + 0 + D=6
f(0) = 6

Answer 19

thats it

Answer 20

So, f(x) = ???

Answer 21

VBG: Please summarize your result:

f(x) = ?? If you're tied up with something else, or prefer not to do this, please just say so.

Answer 22

so f(x) = -sin (x) + 2(x) + D ?

Answer 23

sorry about the delay

Answer 24

D= 6 and C= 2 for f'(x)

Answer 25

Yes, and y ou've found that D=6
so you end up with f(x)=-sin x +2x +6, right? You could check this by differentiating, if you want to.
Any other concerns related to this homework problem?

Answer 26

ah ok so I put 6 instead of D. got it.

Answer 27

No mathmale thats it. Thank you so much for your help

Answer 28

You're very welcome. De nada. Hope to "meet" with you on OpenStudy again soon.
Great day to you. Bye.

Answer 29

Certainly. Thanks again!