Question

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

Answer 1

B. y = e^(-2/x).

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).