Posts Tagged ‘arctangent differential equation’

Some of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients. Because the DE are integrable, therefore one must have an integral formulation for solving the physical problems. This paper introduces Bernoulli integral to complete the Tables of Integral for all of the Mathematical Handbooks.

Basically, the Bernoulli integral is integral form of the homogeneous Bernoulli differential equation (BDE) of constant coefficients. Under proper transformation, the Bernoulli integral can be used to generate another integral formulation especially for integrals that can be transformed into arctangent DE. By using the Bernoulli integral, one can create its self the integral formulation of solving the physical problems, and hence reduces utilization the tables of integral. A special application in generating Euler formula also presented.


Some of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients For instance, in designing electromagnetic apparatus [Markus,1979], the logistic growth process [Welner,2004], chaotic behavior [Barger et al,1995], the generation and propagation of soliton [Wu et al 2005],[Morales,2005], the transport of fluxon [Gonzile et al,2006], the generation of squeezed laser [Friberg,1996 ],etc. One requires Table of Integral to solve a specific integral for solving such differential equation [Spiegel,MR,1968]. To complete the Table of integral, we introduce Bernoulli integral that until now not including in both of the Table integral and mathematical Handbook. By using the Bernoulli integral, one can create the integral formulation required in solving the physical problems, and hence reduces utilization the Tables of integral.

For Detail Visit :

  1. New Science Future (http://rohedi.blogspot.com)
  2. ROHEDI Laboratory (http://rohedi.com)

Read Full Post »

Existence of the universe is reality evidence of supremacy and science fame of God Allah SWT. Inking seven of times water in all ocean world (even more) not enough to write down it. According to writer, mathematical model which representatively as stepping in developing the Islamic Scientific is arctangent differential equation


which its exact solution is of the form:



Because of writer looks into this arctangent differential equation is having the religion character
(according to writer that for a=1, b=1, and both of initial values t0 = 0 dan y0 = 0 the value -.gif of the tangent function at fungsi_tan.gif correspond to the Qidam and Baqa properties), hence solution yielded a solver technique entering religion factors must still appropriate to the exact solution

This paper introduces a new technique of solving a nonlinear first order ordinary differential equation so-called as SMT (stands for Stable Modulation Technique) which its solution is in the form of AF(A), that is a formula of modulation function which its amplitude term is also including in the phase function. The transfromation function applied for solving eq.(1) by using SMT is jihat_image4.gif what gives its final solution in the form :



The idea of developing this stable modulation technique based on the event of Isra’ and Mi’raj of prophet Muhammad, which alongside its journey towards Sidhratulmuntaha guided by angel Jibril. Eqs.(3) assures writer that when mi’raj the energy of prophet Muhammad is transferred into the energy form of modulated wave. The fundamental aspect for developing of modern mathematics and computing is obtained when to = 0, yo = 0, a = 0 dan b = 0 where eq.(3) then reduces to the form :

Eqs .(4)

Eqs.(4) as a representative form of tangent function up to now has not been met in Mathematics Handbook, because the only

Eqs .(5)

But both of eq.(4) and eq.(5) are still giving the same value with the value of tan(t) for all values of t except at t = pi / 2 in eq.(4) and at t = pi in eq.(5) which both giving value of 0/0, though value of tan(pi/2) = ~. In mathematics the value of 0/0 is unknown as commonly called as NaN (stands for Not a Number). The value of ~ is still not obtaining from eq.(4) and eq.(5), even if has been performed the limit operation because it is only giving devide by zero:

Eqs .(6)

At presentation of the exact solution of arctangent differential equation brightens the confidence of writer that during journey Isra’, angel Jibril telling the exact properties of God, while during journey Mi’raj of prophet Muhammad is supplied by a stabilization of believe that God doesn’t spell out members as apparently at 0/0, and man will never can reach God will desire, as apparently at 1/0. The primary message is that mathematics applied as “approach” properly in the effort of explaining the Sunnatullah, and don’t make mathematics as a justification tool.

Read Full Post »