The differential equation satisfies and

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

Problem

The differential equation dydx=k yx(x−4)\displaystyle \frac{dy}{dx}=\frac{k\,y}{x(x-4)} satisfies y(2)=3y(2)=3 and y(3)=4y(3)=4. What is the value of the constant kk? (a) 4ln⁡(4/3)ln⁡3\dfrac{4\ln(4/3)}{\ln 3} (b) −ln⁡(4/3)ln⁡3-\dfrac{\ln(4/3)}{\ln 3} (c) −4ln⁡(4/3)ln⁡3-\dfrac{4\ln(4/3)}{\ln 3} (d) −4ln⁡(4/3)-4\ln(4/3)

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