Page 58 - 4549

a  v 2 akt
As 0(v )  0 C  0 then ln 
1
a  v m
akt akt

e m  e m akt kg
from where v  a  ath  ath t
akt akt
 m m
e m  e m
.
Thus, for determination of function (ts ) we have equation:
ds kg
 ath t .
dt m

Integrating we find
m kg
s  lnch t  C .
2
k m

As 0(s )  0 C 2  0 then the sought law after of motion has
a kind
m kg
s  ln ch t .
k m

3.2.3 Differential Equation of a Kind
F (y ,  y ,  y ,..., y (n ) )  0 .

We will consider differential equation of n-th order, which
does not contain the independent variable of x obviously:
F (y ,  y ,  y ,..., y (n ) )  0 . (3.12)
In this case always it can bring an order down of equation
on unit, entering a new unknown function (yp )  , y where
y we take for an argument. Derivatives y  , y  ,..., y (n ) it is
needed to express through derivative this new function on an
argument y taking into account the rule of differentiation of the
built function:
56