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1.9.32 Solve first order differential equations (A-level only)

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Question 5
a.

Express 7x+3(x−1)(3x+2)\displaystyle \frac{7x + 3}{(x - 1)(3x + 2)}(x−1)(3x+2)7x+3​ in partial fractions

[3]
b.

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

(x−1)(3x+2)dydx=y(7x+3) (x - 1)(3x + 2) \frac{dy}{dx} = y(7x + 3) (x−1)(3x+2)dxdy​=y(7x+3)
[5]
c.

Hence find the particular solution to the differential equation that satisfies y=12y = 12y=12 at x=2x = 2x=2, giving your answer in the form y=f(x)y = f(x)y=f(x)

[4]

1.9.32 Solve first order differential equations (A-level only) Questions

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