The differential equation is subject to the initial condition

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

The differential equation dydx=(y−1)(y+2)\dfrac{dy}{dx} = (y-1)(y+2) is subject to the initial condition y(0)=0y(0)=0. Which of the following is the explicit solution satisfying the condition on the interval where it is defined? (a) y=2(1+e3x)2−e3xy = \dfrac{2(1 + e^{3x})}{2 - e^{3x}} (b) y=2(1−e3x)2+e3xy = \dfrac{2(1 - e^{3x})}{2 + e^{3x}} (c) y=1−2e3xy = 1 - 2e^{3x} (d) y=−2(1−e3x)2+e3xy = -\dfrac{2(1 - e^{3x})}{2 + e^{3x}}

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