Question

Solve the differential equation dy dx – 3y cot x = sin 2x given y = 2 when x = π 2

Answer 1

Things to know :

1) First order linear differential equation .
To find integrating factor (IF) of this equation .


2) d (-cosec x) = cot x cosec x.

3) Integral of cot x = ln sin (x) + C where C is arbitrary constant .

Final Result :
$\frac{y}{ { \sin(x) }^{3} } = - 2 \csc(x) + c \: \: where \: c \\ is \: constant \: of \: integration$