Question

√x +√y * dy/dx = 0 when y(1)=4. Find the solution of the differential equation that will satisfy the condition. Differential equations. I understand how to separate the variables, but I'm not sure where/when it might make sense to square the equation to get rid of the square roots.

Answer 1

Usually you do that when you try to solve for y explicitly.

Answer 2

Meaning?

Answer 3

Separate your variables, integrate normally, solve for y (don't forget that you'll have a constant), apply your initial conditions to solve for that constant, done.

Answer 4

So I got √y * dy = -√x * dx then I integrated and got (2y^(3/2))/3 = (-2x^(3/2))/3 Is that correct so far?

Answer 5

yes, don't forget the constant. The constant here for you to find the particular solution in addition to general solution

Answer 6

So the integration is correct and now I added C to to the right side of the equation and now I need to substitute 1 in for x and solve??

Answer 7

i didnt look at your integration. But, the steps are correct. Yes

Answer 8

My integration might be wrong xD. Or at least I'm about it.

Answer 9

ugh

Answer 10

sorry right

Answer 11

(GAH!!) So where'd I go wrong?

Answer 12

did u substitute y=4 x=1, or where exactly u got wrong?

Answer 13

I didn't substitute in y=4 x=1 until after integration.

Answer 14

do have answer?

Answer 15

I don't have the integration right though.