Can Nonlinear ODEs with Complex Coefficients Be Solved Explicitly?

[luna_aaa]

dy(t)/dt= c1* y(t) + 1 - c2*f(c3*y(t))

Here c1>0, c2 is a complex number but |c2|<=1, c3>0,

f(c3*y(t)) is a nonlinear function of c3*y(t).

The initial value is given by y(s)=0.

Is it possible to be solved?

 

[d_leet]

I think that any solution will be highly dependant on the function f(c3*y(t)), and in most cases there will probably be no anylitic solution to the equation.

 

[luna_aaa]

I think that any solution will be highly dependant on the function f(c3*y(t)), and in most cases there will probably be no anylitic solution to the equation.

what about an exponential for the "f" function?

 

[kosovtsov]

Since your DE admit separation of variables, the solution of your DE (in implicite form) with your initial value is as follows

t-s-\int_0^{y(t)}\frac{dz}{zc1+1-c2f(zc3)}=0 .