Abel Differential Equation of the Second Kind (Special Case). 25. yy' x = f(x)y + g(x). Abel differential equation of the second kind (special case). 1 ...

Abel Differential Equation of the Second Kind. 26. yy' x = f(x)y2 + g(x)y + h(x). Abel differential equation of the second kind. 1◦ . The substitution y = E ...

In this paper, we introduce a new functional relation between the variable coefficients that can lead to the general solutions of the above Abel equation.

The Abel equation of the second kind is given by(1) [ g 0 ( x ) + g 1 ( x ) w ] w ′ = f 0 ( x ) + f 1 ( x ) w + f 2 ( x ) w 2 .

By using appropriate transformations, expressions of Abel dynamic equations of second kind are derived on the general time scale. This also leads to a specific ...

Abstract. In this paper, we propose a direct method to obtain an implicit solution of the Abel equation of the second kind.

Various classes of Abel equations of the second kind are solvable under special conditions and can now be translated into conditions to solve Abel equations of ...

This paper is dedicated to present an exact solution for a nonlinear differential equation so-called. Abel equation. This equation was known as one of the ...

22 окт. 2024 г. · By using appropriate transformations, expressions of Abel dynamic equations of second kind are derived on the general time scale. This also ...

17 дек. 2017 г. · Hint: Approach 1: 4(y(z)+z2)y′(z)−(1+6z)y(z)=0. 4(y+z2)dydz=(6z+1)y. Let x=z4 ,. Then dydz=dydxdxdz=14dydx. ∴(y+16x2)dydx=(24x+1)y.