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1.8.11 Differential equations with separable variables (A-level only)

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Question 8
a.

Express 3x−3(x+1)(2x−1)\displaystyle \frac{3x - 3}{(x + 1)(2x - 1)}(x+1)(2x−1)3x−3​ in partial fractions

[3]
b.

Given that x>1x > 1x>1, find the general solution to the differential equation

(x+1)(2x−1)dydx=y(3x−3) (x + 1)(2x - 1) \frac{dy}{dx} = y(3x - 3) (x+1)(2x−1)dxdy​=y(3x−3)
[5]
c.

Hence find the particular solution to the differential equation that satisfies y=6y = 6y=6 at x=5x = 5x=5, giving your answer in the form y=f(x)y = f(x)y=f(x)

[4]

1.8.11 Differential equations with separable variables (A-level only) Questions

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