Question

Construct a tangent field for y' = 2sqroot(y). Note that necessarily y>0 y' > 0
Find all solutions of y' = 2sqroot(y) as in the treatment of eq. 4 in the text
How many solutions are there through each point on the x-axis? Each point off the x-axis?

Answer 1

And here's the book that I'm using...section 1.3 page 12
http://scholarspace.manoa.hawaii.edu/handle/10125/21735

Also, I'll be putting up the tangent field and what I got in paint shortly.

Answer 2

There are many solutions on the x-axis, but it's only on the top part of the plane in the tangent field.

Answer 3

done...so yeah the book is cray cray

Answer 4

it goes according to separating the values like one side for dy and one side for dx

Answer 5

not separating the values. variables.

Answer 6

So: \[
\frac {y'}{\sqrt y} =2
\]?

Answer 7

I did the tangent field of it which was no problem. the issue comes in when I have to use separate variables to get to the answer.

Answer 8

you know how y' becomes dy/dx

Answer 9

Okay so separation of variables.