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Given the equation:

dy/dx = (x/y)

I know we would initially go to:

∫dy =∫ (x/y) dx

then too:

∫(y)(dy) = ∫x dx

Until arriving at:

(y^{2}/2) + C_{1}= (x^{2}/2) + C_{2}

(y^{2}) - (x^{2}) = C

My question is:

Where does the dy disappear to in step 4? Where the anti-derivative is taken.

Why does ∫dy become just y when solving an equation of the form

dy/dx = (x^{2}+ 1), but it disappears in the first example?

Thank you~

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# Basic Differential Equations

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