Maths with David

    9709. P3. Differential Equations. Past Exam Questions

    9709/31/M/J/25q10 – Mark Scheme

    (a) Find the quotient and remainder when x^3 + 5x^2 - 2x - 15 is divided by x^2 - 3 [3 marks]

    (b) The variables x and y satisfy the differential equation \frac{dy}{dx} = \frac{x^3 + 5x^2 - 2x - 15}{ 6y(x^2 - 3)} .

    It is given that y=2 when x=2.

    Solve the differential equation to solve an expression for y2 in terms of x. [5 marks]

    9709/32/M/J/25q8 – Mark Scheme

    The variables x and \theta satisfy the differential equation sin 2 \theta \frac{dx}{d \theta} = (4x+3) cos 2 \theta , and x = 0 when \theta = \frac{1}{12} \pi .

    Solve the differential equation and obtain an expression for x in terms of \theta . [7 marks]

    9709/33/M/J/25q10 – Mark Scheme

    The variables x and y satisfy the differential equation sin4y \frac{dy}{dx} = x sin2y sin3x .

    It is given that y = \frac{1}{12} \pi when x = \frac{1}{2} \pi .

    (a) Solve the differential equation, obtaining a relation between x and y. [8 marks]

    (b) Given that 0 < y < \frac{1}{2} \pi , find the values of y when x = 0. [2 marks]