Question

a. Solve the differential equation y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared.
b. Explain why the initial value problem y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared with y(0) = 4 does not have a solution.

Answer 1

https://gyazo.com/fa06c87f78388c31263201846039dc26

Answer 2

So... go ahead, show me you aren't clueless XD

Answer 3

Lol

Answer 4

Not clueless but somewhat stuck

Answer 5

I remember this but still quite lost

Answer 6

How would I solve

Answer 7

\[1-y^2=e^{2x^2+c}\]

Answer 8

For C?

Answer 9

Need a refreshing mint

Answer 10

What in the world...
haha
To be honest, I haven't even started trying to solve it myself :>

Hang on...

Answer 11

Haha

Answer 12

There's a way for sure, just can't seem to remember

Answer 13

\[\Large \frac{dy}{dx}=4x\sqrt{1-y^2}\]

Answer 14

\[\Large \frac {dy}{\sqrt{1-y^2}}=4xdx\]

You got this far?

Answer 15

Yup and integrated.

Answer 16

And you got...?

Answer 17

\[\ln(\sqrt{1-y^2})=2x^2+C\]

Answer 18

Ahh. No.

Answer 19

Not even close :P

Answer 20

Humour me and try differentiating \[\Large \ln \sqrt{1-y^2}\]
You'll see you won't get to the original \[\Large \frac1{\sqrt{1-y^2}}\]

Answer 21

Is that not the original?

Answer 22

\[\frac{ y }{ y^2-1 }\]

Answer 23

No. Chain rule.

Answer 24

And the original is \[\Large \frac1{\sqrt{1-y^2}}\]

Answer 25

Oh

Answer 26

It is a property of inverse sin

Answer 27

Am I right or right?

Answer 28

Finally ^^
\[\Large \sin^{-1}(y) = 2x^2 + C\]

Answer 29

Now what?

Answer 30

Well, the second part of the question.
Show that the initial value y(0) = 4 has no solution.

Answer 31

Should be easy enough?

Answer 32

So wait....that's the end of the first part? No way to make it y=?

Answer 33

I honestly don't think so but sometimes you poop magic out

Answer 34

Magic that makes sense.

Answer 35

Well, you can certainly have \[\Large y = \sin[2x^2 + C]\]

Answer 36

It doesn't really matter.
Now, do the second part. :D

Answer 37

I like that better. Second part it is

Answer 38

You get

Answer 39

\[4=\sin(c)\]

Answer 40

Which can't be solved.

Answer 41

Sehr gut ^^
Very good.

Answer 42

wut?

Answer 43

Sehr gut is "very good" in German :D

Answer 44

TIL

Answer 45

Are we done here? :D