| Exam Board | AQA |
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| Module | Further Paper 2 (Further Paper 2) |
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| Year | 2024 |
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| Session | June |
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| Marks | 4 |
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| Topic | Second order differential equations |
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9 A curve passes through the point (-2, 4.73) and satisfies the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } - x ^ { 2 } } { 2 x + 3 y }$$
Use Euler's step by step method once, and then the midpoint formula
$$y _ { r + 1 } = y _ { r - 1 } + 2 h \mathrm { f } \left( x _ { r } , y _ { r } \right) , \quad x _ { r + 1 } = x _ { r } + h$$
once, each with a step length of 0.02 , to estimate the value of \(y\) when \(x = - 1.96\)
Give your answer to five significant figures.
[0pt]
[4 marks]