Trigonometric Polynomial Solutions of Bernoulli Trigonometric Polynomial Differential Equations

We consider real trigonometric polynomial Bernoulli equations of the form A(θ)y′=B1(θ)+Bn(θ)yn where n≥2, with A,B1,Bn being polynomials degree at most μ≥1 in variables θ and Bn(θ)≢0. also A(θ)yn−1y′=B0(θ)+Bn(θ)yn A,B0,Bn variable For first equation, we show that when n≥4, it has 3 solutions n is even 5 odd. second n≥3, odd even. provide two types mentioned above maximum number achieved. The proof method will be to apply extended Fermat problems equations.