| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2016 |
| Session | Specimen |
| Marks | 6 |
| Topic | Differential equations |
| Type | Separable variables - standard (polynomial/exponential x-side) |
| Difficulty | Standard +0.3 This is a straightforward separable variables question requiring standard integration techniques (∫x^(-2)dx and ∫cos y dy), followed by applying an initial condition to find the constant. While it requires competent algebraic manipulation and making y the subject at the end, it follows a completely standard template with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
Separate variable prior to integration [M1]
$\int \frac{1}{\sec y}\,dy = \int \frac{1}{x^2}\,dx$ [A1]
$\sin y = -\frac{1}{x}$ $(+c)$ [A1]
Substitute in $y = \frac{\pi}{6}$ and $x = 4$ to get $c = \frac{3}{4}$ [M1, A1]
$y = \sin^{-1}\!\left(\frac{3}{4} - \frac{1}{x}\right)$ o.e. [A1]7 Solve the differential equation $x ^ { 2 } \frac { \mathrm {~d} y } { \mathrm {~d} x } = \sec y$ given that $y = \frac { \pi } { 6 }$ when $x = 4$ giving your answer in the form $y = \mathrm { f } ( x )$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2016 Q7 [6]}}