Diff EQ fixed

Calculus Level pending

If y ′ = − y 2 − 6 y 2 x y + 6 x y'=\frac{-y^2-6y}{2xy+6x} and y ( 1 ) = − 3 ± 3 2 y(1)=-3\pm{3\sqrt{2}} compute the integer closest to y ( − 1 ) y(-1)


The answer is -3.

<> <> by <> <> , 21, India

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1 solution

<> <>
Aug 17, 2017

Using the identity that the derivative is the -partial wrt x/ partial wrt y it's immediate the solution is of the form

x y 2 + 6 x y = C xy^2+6xy=C

Obviously C = − 9 C=-9

So we have x y 2 + 6 x y + 9 = 0 xy^2+6xy+9=0

Plugging in one we get ( y + 3 ) 2 = 0 → y = − 3 (y+3)^2=0 \to \boxed{y=-3}

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