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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
integrate both sides
 2 years ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
i multiplied dx on both sides
 2 years ago

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
1/e^{y}=e^{y}
 2 years ago

Denebel Group TitleBest ResponseYou've already chosen the best response.1
Oh ok. Thanks.
 2 years ago

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

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

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1327550585485:dw
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1327550603285:dw
 2 years ago

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
1=1+C 11=C 2=C
 2 years ago

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

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