Question

dy/dx = (cos x)e^(sin x), y(0) = 0, solve the initial value problem

Answer 1

so you to integrate both sides to find y

Answer 2

\[\int\limits_{}^{}\frac{dy}{dx} dx=\int\limits_{}^{}\cos(x)e^{\sin(x)} dx\]

Answer 3

use a sub on the right hand side

Answer 4

are you there?

Answer 5

yes sorry. having computer problems

Answer 6

u sub. would it be u=sinx du=cosx?

Answer 7

well du=cos(x)dx

Answer 8

and yes

Answer 9

\[y=\int\limits_{}^{}e^{u} du\]

Answer 10

answer being e^sin (x) -1 when you plug in initial conditin of y(0) =0 yes?

Answer 11

looks good

Answer 12

thanks!

Answer 13

would dy/dx = x/y be

Answer 14

\[\int\limits y dy = \int\limits x dx\]