QuestionQ5. Find $\frac{d y}{d x}$ when $2 x^{2}-y^{2}=5 x \sin (y)+2 a^{13}$

Studdy Solution
Rearrange the equation to solve for $\frac{dy}{dx}$:
1. Move all terms involving $\frac{dy}{dx}$ to one side of the equation: $ -2y \frac{dy}{dx} - 5x \cos(y) \frac{dy}{dx} = 5 \sin(y) - 4x \]
2. Factor out $\frac{dy}{dx}$: $ \frac{dy}{dx}(-2y - 5x \cos(y)) = 5 \sin(y) - 4x \]
3. Solve for $\frac{dy}{dx}$: $ \frac{dy}{dx} = \frac{5 \sin(y) - 4x}{-2y - 5x \cos(y)} \]
The derivative $\frac{dy}{dx}$ is:
$\frac{dy}{dx} = \frac{5 \sin(y) - 4x}{-2y - 5x \cos(y)}$