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Denebel
 3 years ago
use separation of variables to solve the initial value problem.
dy/dx=(cos x)e^(y+sinx) and y=0 when x=0
Denebel
 3 years ago
use separation of variables to solve the initial value problem. dy/dx=(cos x)e^(y+sinx) and y=0 when x=0

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myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[e^{y} dy =\cos(x)e^{\sin(x)} dx\]

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1Lol.. I don't know how to move "the x with dx" and "y with dy".. :/ can you show me that part?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1i multiplied dx on both sides

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[e^{y+\sin(x)}=e^{y} e^{\sin(x)}\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1divide both sides by e^y

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1How do I integrate cosxe^(sin x) dx?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1ley u=sin(x) => du=cos(x) dx

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1? What about the e? Do I put e to the u power?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[\int\limits_{}^{}e^u du=e^u+C=e^{\sin(x)}+C\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1i replace sin(x) with u and cos(x) dx with du

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1Oh? But don't I integrate dw:1327549907891:dw? What happens with the cos...

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1cos(x) dx=du i replaced cos(x) dx with du i did integrate

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1327550585485:dw

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1327550603285:dw

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1Ohh I see. Ok, what do I do now? Do I plug in the given x, y values to find C?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1have you integrated the other side yet?

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1I have now: e^(y) = e^(sinx) + C

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1ok so enter in (0,0) and solve for C

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1I solved that C = 0, So does the equation become e^(y) = e^(sinx) ?

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1Oh I forgot about the negative on the left.

Denebel
 3 years ago
Best ResponseYou've already chosen the best response.1Then e^(y) = e^(sinx)  2 ?
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