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

1. anonymous

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

2. anonymous

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

3. anonymous

interval integral?

4. anonymous

correct, sorry

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

n here = 1/2

11. anonymous

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

12. anonymous

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