t) Suppose y(x)=7e−2x is a solution of the initial value problem dydx =−ky, y(0)=y0. What are the constants k and y0?
Question
Solution 1
The given function is y(x) = 7e^(-2x).
The constant k is the coefficient of x in the exponent of the exponential function. In this case, k = 2. Note that the negative sign in the exponent is part of the differential equation dy/dx = -ky, so k is positive.
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