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

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

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

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
interval integral?
 2 years ago

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

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

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

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

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

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
n here = 1/2
 2 years ago

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

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