Solve the initial value problems:
1/θ(dy/dθ) = ysinθ/(y^2 + 1); subject to y(pi) = 1

Using separation of variables, it is found that the solution of the initial value problem is:

The differential equation is given by:

Applying separation of variables, we have that:

The first integral is solved applying the properties, as follows:

The second integral is solved using integration by parts, as follows:

Then:

Then:

means that when , which is used to find K.

Then, the solution is:

To learn more about separation of variables, you can take a look at link

Step-by-step explanation:

Given the initial value problem subject to y(π) = 1. To solve this we will use the variable separable method.

Step 1: Separate the variables;

The solution to the initial value problem will be;

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

i think it is 18

step-by-step explanation: