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