anonymous
  • anonymous
use separation of variables to solve the initial value problem. dy/dx=(cos x)e^(y+sinx) and y=0 when x=0
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
myininaya
  • myininaya
\[e^{-y} dy =\cos(x)e^{\sin(x)} dx\]
myininaya
  • myininaya
integrate both sides
anonymous
  • anonymous
Lol.. I don't know how to move "the x with dx" and "y with dy".. :/ can you show me that part?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

myininaya
  • myininaya
i multiplied dx on both sides
myininaya
  • myininaya
\[e^{y+\sin(x)}=e^{y} e^{\sin(x)}\]
myininaya
  • myininaya
divide both sides by e^y
myininaya
  • myininaya
1/e^{y}=e^{-y}
anonymous
  • anonymous
Oh ok. Thanks.
anonymous
  • anonymous
How do I integrate cosxe^(sin x) dx?
myininaya
  • myininaya
ley u=sin(x) => du=cos(x) dx
anonymous
  • anonymous
? What about the e? Do I put e to the u power?
myininaya
  • myininaya
\[\int\limits_{}^{}e^u du=e^u+C=e^{\sin(x)}+C\]
myininaya
  • myininaya
i replace sin(x) with u and cos(x) dx with du
anonymous
  • anonymous
Oh? But don't I integrate |dw:1327549907891:dw|? What happens with the cos...
myininaya
  • myininaya
cos(x) dx=du i replaced cos(x) dx with du i did integrate
myininaya
  • myininaya
|dw:1327550585485:dw|
myininaya
  • myininaya
|dw:1327550603285:dw|
anonymous
  • anonymous
Ohh I see. Ok, what do I do now? Do I plug in the given x, y values to find C?
myininaya
  • myininaya
have you integrated the other side yet?
anonymous
  • anonymous
I have now: -e^(-y) = e^(sinx) + C
myininaya
  • myininaya
ok so enter in (0,0) and solve for C
anonymous
  • anonymous
I solved that C = 0, So does the equation become -e^(-y) = e^(sinx) ?
myininaya
  • myininaya
-1-1=-2
myininaya
  • myininaya
-1=1+C -1-1=C -2=C
anonymous
  • anonymous
Oh I forgot about the negative on the left.
anonymous
  • anonymous
Then -e^(-y) = e^(sinx) - 2 ?
myininaya
  • myininaya
yes
anonymous
  • anonymous
Thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.