Edexcel C4 2018 June — Question 6 6 marks

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2018
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferential equations
TypeSeparable variables - standard (polynomial/exponential x-side)
DifficultyStandard +0.3 This is a straightforward separable variables question requiring standard technique: separate variables, integrate both sides (using substitution u=2x for the right side), apply initial condition, and rearrange for y. While it involves trigonometric integration and algebraic manipulation, it follows a completely standard C4 template with no novel problem-solving required, making it slightly easier than average.
Spec1.08k Separable differential equations: dy/dx = f(x)g(y)

  1. Given that \(y = 2\) when \(x = - \frac { \pi } { 8 }\), solve the differential equation
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } } { 3 \cos ^ { 2 } 2 x } \quad - \frac { 1 } { 2 } < x < \frac { 1 } { 2 }$$ giving your answer in the form \(y = \mathrm { f } ( x )\).

\begin{enumerate}
  \item Given that $y = 2$ when $x = - \frac { \pi } { 8 }$, solve the differential equation
\end{enumerate}

$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y ^ { 2 } } { 3 \cos ^ { 2 } 2 x } \quad - \frac { 1 } { 2 } < x < \frac { 1 } { 2 }$$

giving your answer in the form $y = \mathrm { f } ( x )$.\\

\hfill \mbox{\textit{Edexcel C4 2018 Q6 [6]}}