Bernoulli's ode

Question

When solving the following Bernoulli's ode how do we find r?

Answer 1

We devide by x², we get y' - sinx·y/x² = 1/x²y^-3. Now r = 1-(-3) = 4 and we have to change to function v= y⁴.

Answer: r = 4 and substitution v = y⁴, v' = 4y³y', so if we multiplying equation by 4y³ we get:

v' - 4sinx/x² v = 4/x², which is linear nonhomoginius 1st order ODE

_