1.8.11 Differential equations with separable variables (A-level only)

a.

Find $dx\int x^2 \cos 4x \, dx$

[4]

b.

A satellite's distance $r$ from a planet is modeled by the differential equation

\frac{dr}{d\theta} = \frac{(\theta \sin 2\theta)^2}{r^2}

where $θ\theta$ is the angular displacement in radians.

Hence solve this differential equation to find an expression for $r^3$ in terms of $θ\theta$ .

[5]

a.

Find $dx\int x^2 \cos 4x \, dx$

[4]

b.

A satellite's distance $r$ from a planet is modeled by the differential equation

\frac{dr}{d\theta} = \frac{(\theta \sin 2\theta)^2}{r^2}

where $θ\theta$ is the angular displacement in radians.

Hence solve this differential equation to find an expression for $r^3$ in terms of $θ\theta$ .

[5]

1.8.11 Differential equations with separable variables (A-level only) Questions