Question

If dy/dx = y cos x and y = 3 when x =0, then y=...?

Answer 1

Please explain what i need to do becuase im not even sure how to approach this problem

Answer 2

That is exactly how the question is asked:
If dy/dx = y cos x and y = 3 when x = 0, then y =....? Here are the answer choices

a) e^(sinx) +2
b) e^(sinx) + 3
c) sin x + 3
d) sin x + 3e^x
e) 3e^ (sinx)

Answer 3

Does teh question make more sense now

Answer 4

it looks rather seperable to me

Answer 5

\[\frac{dy}{dx}=ycos(x)\]
\[\int \left(\frac{1}{y}dy=cos(x)dx\right)\]

Answer 6

\[ln(y)=sin(x)+c\]
\[y = Ce^{sin(x)}\]

Answer 7

wait how did u get taht integral

Answer 8

multiply it all by dx/y

Answer 9

basically, your collecting all the y terms to one side and all the x terms to the other and integrating the whole shebang

Answer 10

ok i get that so now hoe did u get y=Ce^sinx

Answer 11

in order to undo the ln; you have to e^ it all

Answer 12

e^ln(y) = y

e^(sin(x)+c) = e^sin(x) e^c

e^c is just some arbitrary constnat still; e^c = C

y = Ce^sin(x)

Answer 13

ok so now how do we find out wat that constant is b/c 2 of the asnwers have 2 and 3 as constants

Answer 14

yeah, they all have something added; look at the results we got; anything added?

Answer 15

oh it has to be e) 3e^sinx becasue thats teh only one with a cosntant being multiplied

Answer 16

thats the short of it yes; or we could test that by making x=0; sin(x)= 0 e^0 = 1; and 3 = C*1; C=3

y = 3e^sin(x)

Answer 17

THANKS ALOT =)

Answer 18

yw

Answer 19

Is this right

Answer 20

what about the detailed explanations are you confused about?

Answer 21

Oh I looked this over a couple more times and understood. I got confused on the step when ln(y)=sinx+C changed to y=Ce^sinx

Answer 22

it makes sense now tho? i just used exponent properties to condense it is all

Answer 23

Yes it makes sense. You worked it out really well