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CAIE A Level Mathematics 9709

Differential equations questions

Exam-style questions on Differential equations, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 4 marksStandardA differential equation is given by (dy)/(dx) = (1 x)/(y). Given that y = 7 when x = 3, find the value of the constant of integration C.
  2. 4 marksStandardSolve the differential equation (dy)/(dx) = (3 x^2)/(y), given that y(1) = 2. Find the value of the constant of integration C.
  3. 3 marksStandardThe volume of water, V litres, in a tank at time t minutes is increasing. The rate of increase of V is directly proportional to t. Initially the tank is empty. After 5 minutes, the volume is 25 litres.
  4. 4 marksStandardFind the general solution of the differential equation (dy)/(dx) = 3 y sec^2 x. Give your answer in the form y = f(x), where f(x) involves an arbitrary constant A.
  5. 5 marksChallengeSolve the differential equation (dy)/(dx) = (4y)/(x) , given that y = 3 when x = 1 . Find the value of y when x = 2 .
  6. 5 marksChallengeA curve satisfies the differential equation (dy)/(dx) = 5y^2. Given that y = 5 when x = 0, find the particular solution for y in terms of x.
  7. 5 marksChallengeSolve the differential equation (dy)/(dx) = (3 y^2)/(x), given that y=1 when x=1. Find y in terms of x.