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

1. dumbcow Group Title

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 Group Title

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

3. Algebraic! Group Title

interval integral?

4. S Group Title

correct, sorry

5. dumbcow Group Title

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

6. Algebraic! Group Title

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

7. dumbcow Group Title

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

8. S Group Title

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

9. Algebraic! Group Title

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

10. Algebraic! Group Title

n here = 1/2

11. S Group Title

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

12. dumbcow Group Title

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