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  • Perplex
    IB Math AAHL
    /
    Differential Equations
    /

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    Problem Bank - Differential Equations

    Access custom-built, exam-style problems for differential equations. Each problem has a full solution and mark-scheme, as well as AI grading and support.

    36 Problems Available

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    IB: 4
    1

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    0 / 7

    The curve of y=f(x) is positive definite and satisfies the differential equation dxdy​=yex. It is given that f(0)=1.

    1. Use Euler's method with a step length of h=0.5 to estimate the value of f(2).

      [3]
    2. By solving the differential equation, find f(x).

      [4]
    2

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    0 / 6

    1. Solve the differential equation dxdy​=−yx​.

      [3]

    (12,35) lies on this curve, as does (0,a), where a>0.

    1. Find a.

      [3]
    3

    !

    0 / 8

    A cylindrical oil tank initially contains 256L of oil. Oil leaks from the tank so that the volume V (L) at time t (h) satisfies the differential equation

    dtdV​=−kV43​

    where k is a positive constant. After 8hrs, there are 16L remaining in the tank.

    1. Show that V(t)=(4−4t​)4.

      [6]
    2. Determine how long it takes for the tank to empty.

      [2]
    4

    0 / 5

    1. Solve the differential equation dxdy​=y2x3​.

      [3]

    It is given that y(0)=3.

    1. Find y(2).

      [2]