3 2y = x2. – – (8) (b) Find the particular solution for which, at = 0, = 2 and = 3. x y (6) [FP1 January 2008 Qn 7] 14. (a) Find, in terms of the general solution of the differential equation k, + 4 + 3x = + 5, where is a constant and > 0. kt k t (7) For large values of this general solution may be approximated by a linear function. t, (b) Given that = 6, find the equation of this linear function. k (2) [FP1 June 2008 Qn 4] 15. (x2 + 1) = 2y2 + (1 2x). (I) – (a) By differentiating equation (I) with respect to show that x, (x2 + 1) = (1 4x) + (4y 2). – – (3) Given that = 1 and = 1 at = 0, y x (b) find the series solution for in ascending powers of up to and including the term in y, x, x3. (4) (c) Use your series to estimate the value of at = giving your answer to two decimal y x –0.5, places. (1) [FP3 June 2008 Qn 3]
3 – – 2y = x2. (8) (b) Find the particular solution for which, at x = 0, y = 2 and = 3. (6) [FP1 January 2008 Qn 7] 14. (a) Find, in terms of k, the general solution of the differential equation + 4 + 3x = kt + 5, where k is a constant and t > 0. (7) For large values of t, this general solution may be approximated by a linear function. (b) Given that k = 6, find the equation of this linear function. (2) [FP1 June 2008 Qn 4] 15. (x2 + 1) = 2y2 + (1 – 2x). (I) (a) By differentiating equation (I) with respect to x, show that (x2 + 1) = (1 – 4x) + (4y – 2). (3) Given that y = 1 and = 1 at x = 0, (b) find the series solution for y, in ascending powers of x, up to and including the term in x3. (4) (c) Use your series to estimate the value of y at x = –0.5, giving your answer to two decimal places. (1) [FP3 June 2008 Qn 3]
2de-qns-past-papers.docx