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

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dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0use algebra to get "t" terms with dt on one side, and "y" terms with dy on other side you might try crossmultiplying here

S
 3 years ago
Best ResponseYou've already chosen the best response.0thanks, I know that step, right now I am stuck with interval part

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok, you didn't say so i thought i'd start from beginning :) im guessing the sqrt(y+1) part

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0if you can't do the 'y' part in your head... use u=y+1 du =dy \[{ \int\limits_{}^{}} \sqrt{u} du =?\]

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0sqrt is 1/2 power ... just use power rule

S
 3 years ago
Best ResponseYou've already chosen the best response.0so I get 1/2(y+1)^1/2=t^2/2 ?

Algebraic!
 3 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{ }^{ } x ^{n} = \frac{ 1 }{ n+1 } * x ^{n+1}\]

S
 3 years ago
Best ResponseYou've already chosen the best response.0i got 2/3(Y+1)^3/2=t^2/2, right?

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0yes ... but don't forget constant "+C" on right side
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