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



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dumbcow
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use algebra to get "t" terms with dt on one side, and "y" terms with dy on other side
you might try crossmultiplying here

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

Algebraic!
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interval
integral?

S
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correct, sorry

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

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

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

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

Algebraic!
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\[\int\limits_{ }^{ } x ^{n} = \frac{ 1 }{ n+1 } * x ^{n+1}\]

Algebraic!
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n here = 1/2

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

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