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

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Question 11
a.

Express 5x−15(x+1)(2x−3)\displaystyle \frac{5x - 15}{(x + 1)(2x - 3)}(x+1)(2x−3)5x−15​ in partial fractions

[3]
b.

Given that x>2x > 2x>2, find the general solution to the differential equation

(x+1)(2x−3)dydx=y(5x−15) (x + 1)(2x - 3) \frac{dy}{dx} = y(5x - 15) (x+1)(2x−3)dxdy​=y(5x−15)
[5]
c.

Hence find the particular solution to the differential equation that satisfies y=32y = 32y=32 at x=2x = 2x=2, giving your answer in the form y=f(x)y = f(x)y=f(x)

[4]

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

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