The solution of dy/dx = −6y with y(0) = 3 is
Answer and explanation
Correct answer: A. y = 3e^(−6x)
- Step 1: This is separable: dy/y = −6 dx, so ln y = −6x + C. Step 2. With y(0) = 3 the solution is y = 3e^(−6x). Answer: y = 3e^(−6x). Why not the others: y = 3e^(6x) is what you get if you get the sign of the exponent wrong. y = 3 − 6x is what you get if you assume a linear solution. y = 3e^(−x/6) is what you get if you invert the coefficient.
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