Find the specific solution of the differential equation dy/dx equals the quotient of 2 times y and x squared with condition y(-2) = e. (4 points)

a. y equals negative 1 minus 2 divided by x

b. y equals e raised to the negative 2 over x power

c. y equals negative 1 times e raised to the 1 over x power

d. none of these

B.   y = e^(-2/x).

Step-by-step explanation:

dy/dx = 2y / x^2

Separate the variables:

x^2 dy = 2y dx

1/2 * dy/y =  dx/x^2

1/2  ln y = = -1/x  + C

ln y = -2/x +  C

y = Ae^(-2/x)  is the general solution ( where A is a constant).

Plug in the given conditions:

e = A e^(-2/-2)

e = A * e

A = 1

So the specific solution is y = e^(-2/x).

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