A-LevelMathematicsDifferential equations9709/32 · Oct/Nov 2017 · Q57 Marks
The variables x and y satisfy the differential equation (x + 1) dy/dx = y(x + 2), and it is given that y = 2 when x = 1. Solve the differential equation and obtain an expression for y in terms of x.
- The variables x and y satisfy the differential equation (x + 1) dy/dx = y(x + 2), and it is given that y = 2 when x = 1. Solve the differential equation and obtain an expression for y in terms of x.[7]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [1] Separate variables and obtain ∫ (1/y) dy = ∫ ((x + 2) / (x + 1)) dx
- [1] Obtain term ln y
- [1] Use an appropriate method to integrate (x + 2) / (x + 1)
- [1] Obtain integral x + ln(x + 1), or equivalent, e.g. ln(x + 1) + x + 1
- [1] Use x = 1 and y = 2 to evaluate a constant, or as limits
- [1] Obtain correct solution in x and y in any form e.g. ln y = x + ln(x + 1) – 1
- [1] Obtain answer y = (x + 1)e^(x-1)
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