| Exam Board | Edexcel |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Topic | Second order differential equations |
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15. (a) Find the value of \(\lambda\) for which \(\lambda x \cos 3 x\) is a particular integral of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 9 y = - 12 \sin 3 x$$
(b) Hence find the general solution of this differential equation.
The particular solution of the differential equation for which \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2\) at \(x = 0\), is \(y = \mathrm { g } ( x )\).
(c) Find \(\mathrm { g } ( x )\).
(d) Sketch the graph of \(y = \mathrm { g } ( x ) , 0 \leq x \leq \pi\).
[0pt]
[P4 January 2003 Qn 7]