Question

use separation of variables to solve the initial value problem.

dy/dx=(cos x)e^(y+sinx) and y=0 when x=0

Answer 1

\[e^{-y} dy =\cos(x)e^{\sin(x)} dx\]

Answer 2

integrate both sides

Answer 3

Lol.. I don't know how to move "the x with dx" and "y with dy".. :/ can you show me that part?

Answer 4

i multiplied dx on both sides

Answer 5

\[e^{y+\sin(x)}=e^{y} e^{\sin(x)}\]

Answer 6

divide both sides by e^y

Answer 7

1/e^{y}=e^{-y}

Answer 8

Oh ok. Thanks.

Answer 9

How do I integrate cosxe^(sin x) dx?

Answer 10

ley u=sin(x) => du=cos(x) dx

Answer 11

? What about the e?
Do I put e to the u power?

Answer 12

\[\int\limits_{}^{}e^u du=e^u+C=e^{\sin(x)}+C\]

Answer 13

i replace sin(x) with u
and cos(x) dx with du

Answer 14

Oh? But don't I integrate ? What happens with the cos...