I have a differential equation:
Here $K>0$ is a fixed constant and $f(x)$ is some (as yet) unknown function of $x$, which is in our hands to chose.
What I want is that I should decide $f(x)$ suitably to find a solution $y(x)$ of the above with the condition $y(0)=1$ where $y(x)$ is a rational function of $x$, i.e. a quotient of two polynomials. The solution should not be free of $K$.
I tried setting $f(x)$ so that the coefficient of $K$ becomes $1$ but the differential equation turned out to be so complicated that I could not solve it.
Can anyone offer any help or suggestions please?