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AS & A Level · AS/A Level

Further Mathematics

Second-order differential equations

Name: ____________________Date: October 10, 2026
  1. 1.

    Solve y'' - 3y' + 2y = 0 with y(0) = 3 and y'(0) = 4.

    [3 marks] · no calculator
  2. 2.

    Find the general solution of y'' - 4y' + 4y = 0 and explain why two constants are needed.

    [3 marks] · no calculator
  3. 3.

    Solve y'' + 2y' + 5y = 0 with y(0) = 1 and y'(0) = 0. State the long-term behaviour.

    [3 marks] · no calculator
  4. 4.

    Find the general solution of y'' - y = 6e^(2x).

    [3 marks] · no calculator
  5. 5.

    Solve y'' + 4y = 8cos(2x), with y(0) = 0 and y'(0) = 0. Explain why a trial C cos(2x) fails.

    [3 marks] · no calculator
  6. 6.

    Find all solutions of y'' + y = 0 on [0,pi] satisfying y(0) = 0 and y(pi) = 0. Explain whether these conditions determine a unique solution.

    [3 marks] · no calculator

Original, unofficial practice questions from SubjectScout — not official past-paper questions.

Marking points are indicative, not an official mark scheme. Accept equivalent valid methods and supported interpretations that address the task; award each mark once without requiring the model wording.