1st order differential equation question Watch

Drysteak
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#1
Report Thread starter 9 years ago
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can someone explain how to do the 1st order differential equation, 'dy/dx = (y^2 - 1)/e^0.5x'

i more or less get how to do it, its just the answer im getting wont turn into the one in the back of my book, and i'm not certain why.
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miml
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can you post some working?
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Drysteak
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Ah okay I didn't think to use partial fractions to integrate the LHS, as i got the RHS but couldnt get the LHS to be correct.

Many thanks.
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eulerwaswrong
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(Original post by Lou Reed)
\frac{dy}{dx} = \frac{(y^2 -1)}{e^{\frac{1}{2}}}

first separate the variables and integrate, so:

 \displaystyle\int \frac{1}{y^2 -1} \cdot dy = \displaystyle\int e^{\frac{-1}{2}} \cdot dx

then you have to partial fraction the LHS to integrate it...

 \frac{1}{2}\ln|\frac{y-1}{y+1}| = -2e^{\frac{-1}{2}} + C

thats what i get anyway, hope its right
that look right to me - the bit to spot is the partial fractions bit.

PS. any problems with maths these days use wolfram alpha

http://www58.wolframalpha.com/input/...F%28y%5E2-1%29
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