A-LevelMathematicsDifferential equations9709/33 · May/June 2019 · Q57 Marks
The variables x and y satisfy the differential equation (x + 1)y dy/dx = y² + 5. It is given that y = 2 when x = 0. Solve the differential equation obtaining an expression for y² in terms of x.
- (i)The variables x and y satisfy the differential equation (x + 1)y dy/dx = y² + 5. It is given that y = 2 when x = 0. Solve the differential equation obtaining an expression for y² in terms of x.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] Separate variables correctly and integrate at least one side
- [B1] Obtain term ln(x+1)
- [M1] Obtain term of the form a ln (y² +5)
- [A1] Obtain term (1/2)ln(y² +5)
- [M1] Use y = 2, x = 0 to determine a constant, or as limits, in a solution containing terms a ln(y² +5) and b ln(x+1), where ab ≠ 0
- [A1] Obtain correct solution in any form
- [A1] Obtain final answer y² = 9(x+1)² -5
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