# What is a solution to the differential equation #dy/dx =( 2csc^2 x)/ (cot x)#?

##### 2 Answers

#### Explanation:

The equation simplifies:

Separate variables:

Integrate:

#### Explanation:

First we should separate the variables, which means that we can treat

#dy=(2csc^2x)/cotxdx#

Now integrate both sides:

#intdy=2intcsc^2x/cotxdx#

On the right hand side, let

#y=-2int(-csc^2x)/cotxdx#

#y=-2int(du)/u#

#y=-2lnabsu+C#

#y=-2lnabscotx+C#

One possible simplification we could make if we wanted would be to bring the

#y=2lnabstanx+C#