anonymous
  • anonymous
If dy/dx = y cos x and y = 3 when x =0, then y=...?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Please explain what i need to do becuase im not even sure how to approach this problem
anonymous
  • anonymous
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)
anonymous
  • anonymous
Does teh question make more sense now

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amistre64
  • amistre64
it looks rather seperable to me
amistre64
  • amistre64
\[\frac{dy}{dx}=ycos(x)\] \[\int \left(\frac{1}{y}dy=cos(x)dx\right)\]
amistre64
  • amistre64
\[ln(y)=sin(x)+c\] \[y = Ce^{sin(x)}\]
anonymous
  • anonymous
wait how did u get taht integral
amistre64
  • amistre64
multiply it all by dx/y
amistre64
  • amistre64
basically, your collecting all the y terms to one side and all the x terms to the other and integrating the whole shebang
anonymous
  • anonymous
ok i get that so now hoe did u get y=Ce^sinx
amistre64
  • amistre64
in order to undo the ln; you have to e^ it all
amistre64
  • amistre64
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)
anonymous
  • anonymous
ok so now how do we find out wat that constant is b/c 2 of the asnwers have 2 and 3 as constants
amistre64
  • amistre64
yeah, they all have something added; look at the results we got; anything added?
anonymous
  • anonymous
oh it has to be e) 3e^sinx becasue thats teh only one with a cosntant being multiplied
amistre64
  • amistre64
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)
anonymous
  • anonymous
THANKS ALOT =)
amistre64
  • amistre64
yw
Rea201
  • Rea201
Is this right
amistre64
  • amistre64
what about the detailed explanations are you confused about?
Rea201
  • Rea201
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
amistre64
  • amistre64
it makes sense now tho? i just used exponent properties to condense it is all
Rea201
  • Rea201
Yes it makes sense. You worked it out really well

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