Standard +0.8 This is a standard integrating factor problem from Further Maths FP2, requiring identification of the linear form, calculation of integrating factor involving ∫2cot(2x)dx = ln|sin(2x)|, then integration of sin(x)sin(2x) using product-to-sum formulas. While methodical, it demands careful trigonometric manipulation and integration beyond standard A-level, placing it moderately above average difficulty.
Find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + 2 y \cot 2 x = \sin x , \quad 0 < x < \frac { \pi } { 2 }$$
giving your answer in the form \(y = \mathrm { f } ( x )\).
(Total 7 marks)
Find the general solution of the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } + 2 y \cot 2 x = \sin x , \quad 0 < x < \frac { \pi } { 2 }$$
giving your answer in the form $y = \mathrm { f } ( x )$.\\
(Total 7 marks)\\
\hfill \mbox{\textit{Edexcel FP2 2005 Q2 [7]}}