Question

y' + ytanx=secx. solve the differential equation

Answer 1

Integrate using methods of integrating factors

Answer 2

i have been trying this problem but keep getting it wrong

Answer 3

what did you get mu(t) as?

Answer 4

i meant \[\mu(t)\]

Answer 5

tanx

Answer 6

can you explain please

Answer 7

Ok. This might not be the best medum to explain, but ill try

Answer 8

You equation is already in standard form, which is
\[\frac{ dy }{ dx }+p(x)y=g(x)\]

Answer 9

The best way to solve any equation of this form is to use the method of integrating factors. But for that you have to find mu(t) which will be represented in the equation below as that funny u

Answer 10

i meant to say mu(x) by the way

Answer 11

\[\mu(x)=\exp \int\limits_{}^{} p(x)\]

Answer 12

so locate p(x) from your diff eq, then find mu(t)

Answer 13

mu(x) rather

Answer 14

hm ,still getting the wrong one

Answer 15

I didnt say that was the final answer though, that was just a process. What did you get as mu(x), or what method are you using to solve this?

Answer 16

secx

Answer 17

Ok good. The next thing is to multiply across the mu(x) across your equation, and the use the reverse product rule(your professor should have taught you this), so basically you should get an equation that looks like:\[\int\limits_{}^{}\frac{ dy }{ dx }(secx *y)dx=\int\limits_{}^{}\sec^2(x)dx\]

Answer 18

Does that make sense?

Answer 19

hello?

Answer 20

i got it

Answer 21

totally makes sense now

Answer 22

sorry took me a while

Answer 23

thanks!

Answer 24

Alright, im always glad to help. Dont forget the medal lol