Question

Consider the diff eq dy/dt = ((e^y)*sin(t)^2)/y*sec(t))

Answer 1

considering it...

Answer 2

My work thus far is y*dy/dt = e^y sin^2(t)/sec(t) how do I switch e^y to the other side?

Answer 3

do I multiply by ln(e^y)?

Answer 4

is that
\[\sin^2(t)\]
or \[sin(t^2)\]

Answer 5

sin^2(t)

Answer 6

ydy/ e^y = sin^2 t cost dt

Answer 7

ok... just to make sure
\[\frac{dy}{dt} = \frac{e^y\sin^2(t)}{y\sec(t)}\]

Answer 8

That is the correct equation

Answer 9

\[ye^{-y}dy = \sin^{2}tcostdt\]

Answer 10

looks like your on the right track with separation of variables. Move the e^y term over to get
\[ye^{-y}dy = \frac{\sin^2(t)}{\sec(t)}\]
simplify the right hand side to get what him1618 has...

Answer 11

now for RHS take u = sin t

Answer 12

integration by parts on the left hand side. U-substitution for the left hand side.

Answer 13

What is the move that allows me to move e^y over

Answer 14

divide by e^y both sides?

Answer 15

multiply both sides by e^{-y}

Answer 16

because 1/e^y = e^-y?

Answer 17

yes

Answer 18

Thanks folks

Answer 19

no probs