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

a.

Express $1(1+4x)(1−x)\frac{1}{(1+4x)(1-x)}$ in partial fractions.

[3]

b.

Hence find the solution of the differential equation

(1+4x)(1-x)\frac{dy}{dx} = \tan y

for the interval $−14<x<1-\frac{1}{4} < x < 1$ , given that $\frac{\pi}{2}$ when $x = 0$ .

Give your answer in the form $sin^n y = f(x)$ where $n$ is an integer to be found.

[6]

a.

Express $1(1+4x)(1−x)\frac{1}{(1+4x)(1-x)}$ in partial fractions.

[3]

b.

Hence find the solution of the differential equation

(1+4x)(1-x)\frac{dy}{dx} = \tan y

for the interval $−14<x<1-\frac{1}{4} < x < 1$ , given that $\frac{\pi}{2}$ when $x = 0$ .

Give your answer in the form $sin^n y = f(x)$ where $n$ is an integer to be found.

[6]

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