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Solve the differential equation: sin(y) * (dy/dx) + (1/x) * cos(y) = x⁴ * cos²(y), where C is an arbitrary constant.

1. x * sec(y) = x⁶ + C
2. 6*x * sec(y) = x + C
3. 6*x * sec(y) = x⁶ + C
4. 6*x * sec(y) = 6*x⁶ + C

Correct answer: 6*x * sec(y) = x⁶ + C

Solution

The substitution v = sec(y) reduces the Bernoulli-type equation to a standard linear ODE, which is then solved using an integrating factor.

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