Standard +0.3 This is a straightforward separable variables question requiring integration by parts for the x sin 3x term. While it involves multiple standard techniques (separation, integration by parts, applying initial conditions), it follows a completely routine procedure with no conceptual challenges or novel insights required. Slightly above average difficulty due to the integration by parts component and algebraic manipulation needed.
7 Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = y ^ { 2 } x \sin 3 x$$
given that \(y = 1\) when \(x = \frac { \pi } { 6 }\). Give your answer in the form \(y = \frac { 9 } { \mathrm { f } ( x ) }\).
7 Solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = y ^ { 2 } x \sin 3 x$$
given that $y = 1$ when $x = \frac { \pi } { 6 }$. Give your answer in the form $y = \frac { 9 } { \mathrm { f } ( x ) }$.
\hfill \mbox{\textit{AQA C4 2012 Q7 [9]}}