The solution of dy/dx = −5y with y(0) = 2 is
Answer and explanation
Correct answer: A. y = 2e^(−5x)
- Step 1: This is separable: dy/y = −5 dx, so ln y = −5x + C. Step 2. With y(0) = 2 the solution is y = 2e^(−5x). Answer: y = 2e^(−5x). Why not the others: y = 2e^(5x) is what you get if you get the sign of the exponent wrong. y = 2 − 5x is what you get if you assume a linear solution. y = 2e^(−x/5) is what you get if you invert the coefficient.
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