Question

Use separation of variables to solve differential equation: dy/dt=t/((y+1)^1/2)), y(1)=3 ???

Answer 1

use algebra to get "t" terms with dt on one side, and "y" terms with dy on other side

you might try cross-multiplying here

Answer 2

thanks, I know that step, right now I am stuck with interval part

Answer 3

interval

integral?

Answer 4

correct, sorry

Answer 5

oh ok, you didn't say so i thought i'd start from beginning :)
im guessing the sqrt(y+1) part

Answer 6

if you can't do the 'y' part in your head... use u=y+1 du =dy
\[{ \int\limits_{}^{}} \sqrt{u} du =?\]

Answer 7

sqrt is 1/2 power ... just use power rule

Answer 8

so I get 1/2(y+1)^-1/2=t^2/2 ?

Answer 9

\[\int\limits_{ }^{ } x ^{n} = \frac{ 1 }{ n+1 } * x ^{n+1}\]

Answer 10

n here = 1/2

Answer 11

i got 2/3(Y+1)^3/2=t^2/2, right?

Answer 12

yes ... but don't forget constant "+C" on right side