Solve the Initial Value Problems (IVP) below:
This is an homogeneous differential equation and it is separable. First, we will divide everything by sin x
Now, we will make the following change:
in the equation  above. Then,
Working with this equation a little bit we get:
Integrating both sides we get:
Using the IVP value given in the problem we will have:
Making the necessary calculations, we will get:
Using this result in  above, we finally arrive at:
Which is the equation we’ve been looking for.
This is also an Homogeneous Differential Equation and it is also separable. Repeating the same steps taken above to separate the variables, we will get the following equation:
Integrating, we get:
Which implies that:
Using the IVP value in  above, we get:
substituting  in  we finally have:
Which is a particular solution for the given Differential Equation.