Question

If dy dx equals cosine squared of the quantity pi times y over 2 and y = 1 when x = 0, then find the value of x when y = 3.

Answer 1

https://i.gyazo.com/ae7b7d7e8b307fc8aa3b0e8211d5c806.png

Answer 2

@jim_thompson5910

Answer 3

rearrange the equation:
\[\frac{ dy }{ \cos ^{2} \left( \frac{ \pi y }{ 2 } \right) } = dx\]
\[\int\limits_{}^{}\sec ^{2}\left( \frac{ \pi y }{ 2 } \right)=\int\limits_{}^{}dx\]

Answer 4

Closed it by accident please ignore.

Answer 5

This should look familiar to you

Answer 6

Solve the differential equation using the integral I have given you and you will be able to compute the values of y and x and then plug in the values given in the problem.

Answer 7

Just a question, what happened to dy?

Answer 8

there should be a dy

Answer 9

Ok

Answer 10

Not sure if I'm doing it right.

Answer 11

I got \[\tan(y \pi/2) = x\]

Answer 12

yes that is what I got too, but looking at it now, I see it doesn't satisfy the condition when y=1, x =0. Let me check and see where the error could be.

Answer 13

Ok, so we're still on the same page.

Answer 14

but also it is multiplied by the constant 2/pi which you get from u-substitution

Answer 15

I'm getting
\[\Large \frac{2}{\pi}\tan\left( \frac{\pi y}{2}\right) = x+C \]
after integration. The problem is that when y = 1, the value of `tan(y*pi/2)=tan(1*pi/2)=tan(pi/2)` is undefined. So that's strange how they say `y = 1 when x = 0`

Answer 16

@jim_thompson5910 that's the same thing I'm getting. Could be an error with the problem

Answer 17

So how would I go about this... it's an automated system so I can't just tell em it doesn't make sense.

Answer 18

Should I just play along?

Answer 19

You'll have to bring it up with your teacher

Answer 20

maybe they want you to use Euler's method here?

Answer 21

Ypu could try to use that equation and plug in the value y=3 and see what you get, but I'm pretty sure the problem has an error at least with the initial condition y=1, x=0

Answer 22

kind of going to be difficult though I think to beat the computer on this one, since you need to solve for C using the initial values, and you have an option of none of these, so you won't be able to be compltetely sure.

Answer 23

I'll think I'm gonna go with none of these, thanks for pointing that out. When I plugged in 3 I got an extremely large number.

Answer 24

@jim_thompson5910 what do you think?

Answer 25

see attached for the slope field of dy/dx = cos^2(pi*y/2)

If y = 1, then dy/dx = 0

Using euler's method, we'd be stuck on the red line of y = 1 no matter what x is. So it appears that y = 3 isn't possible to achieve. So I agree with @VeritasVosLiberabit I would say "none of these" and consult the teacher. This problem seems a bit off. Perhaps there's a typo somewhere?

Then again, since y = 1 makes the f(x,y) function undefined, it is more valid to think of that red line as an asymptote if anything

Answer 26

@VeritasVosLiberabit @jim_thompson5910 Thanks guys, much appreciated.