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:

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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;

the answer is 375 miles

step-by-step explanation: