First order DE: Homogeneous equations

First order DE: Homogeneous equations

General form:

Example:

 

By taking x³ from the first part and the second part as a common factor.

 

 

 

special relativity-New relativity of Einstein

special relativity-New relativity of Einstein

Fundamental postulates:

1) The low of physical phenomena must be the same velocity form in all inertial form (systems).

2) The speed of light is constant and is independent  of motion of the source or the observer.

the Lorentz-einstein transformation

--> at t=0   => O=~O'

after time t

              x' =f(x,t)

              x' =γx+βt: β&γ are constants

--> the origin O' 

             x=ut                        x'=0

             0=γut+βt

             x'=γ(x-ut)

             x=γ(x'+ut')            

             x=γ²(x-ut) + γut’

             x- γ²x+ γ²ut= γut’

                 t’= γt+((1- γ²)/ (γu))x

        where γ =1/√(1-u²/c²)

        γ always > 0

        

        x =γ(x'+ut')

        x=(x'+ut')/√(1-u²/c²)

        y=y'

        z=z'

        t=(t'+(u/c²)x')/√(1-u²/c²)