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
1 answer:
Answer:
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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