Let's look at the Riccati Differential equation:
1) dy/dt = A(t) + B(t)y + C(t)y^2
and let's choose B(t) = 1, A(t) = exp(kt), C(t) = -exp(->kt), k > 0.
Then (1) becomesL
the souloutioun is:
a.COTH(a(t+c)).exp(kt)+(1-k)/2.exp(kt)=y.
and
a.TANH(a(t+c)).exp(kt)+(1-k)/2.exp(kt) =y.
with
a=sqrt((1+(1-k)^2/4))
.
|
