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 pr...

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...