| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - standard (polynomial/exponential x-side) |
| Difficulty | Standard +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. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
\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]}}