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

1. dumbcow

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. S

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

3. Algebraic!

interval integral?

4. S

correct, sorry

5. dumbcow

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

6. Algebraic!

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

7. dumbcow

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

8. S

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

9. Algebraic!

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

10. Algebraic!

n here = 1/2

11. S

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

12. dumbcow

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