Question

Please Help! Solve the IVP dy/dt - (cos t)/(sin t)*y = 2*sin(t) y(pi/2) = 0 We have been using the Integration factor method

Answer 1

its a linear ODE, integrting factor will do

Answer 2

whats your IF here ?

Answer 3

\[\large \rm y' + \left(- \dfrac{\cos t}{\sin t}\right)y = 2\sin t\]

Answer 4

\[\large \rm\text{IF} = e^{\int \frac{-cos t}{\sin t} dt} = ?\]

Answer 5

that's where I get confused it should be e^-csc(t) right...but that makes it super complicated in the end. I don't know what -csc(pi/2) is?

Answer 6

where did you get csc from ?

Answer 7

its not e^-csc(t)

Answer 8

oh...wait sorry -cot (t)

Answer 9

ooops....I keep reading it wrong from wolfram

Answer 10

-cos(t)/sin(t) = -cot(t) and then the integral of -cot(t) is -log(sin(x))

Answer 11

\[\large e^{-\ln(\sin x)}=?\]

Answer 12

-sin(x) ?

Answer 13

\[\large=\left[ e^{\ln(\sin x)} \right]^{-1}\]

Answer 14

=?

Answer 15

(sin x)^-1 = 1/sin(x)

Answer 16

right that's your integrating factor ... you multiply to the original equatiom

Answer 17

ok awesome! I think im right from here thanks! I just got caught up in the integral and trig identities. Need to practise that :)