As far as I know, for an n-th order homogeneous linear differential equation, there are n number of linearly independent solutions and the general solution to the equation is a linear combination of them. In the case of nth order homogeneous non-linear differential equation can it be shown that there are n number independent solutions? Can anybody tell me where I can find details of this? In case there are n number of independent solutions, I am not sure how to write the general solution. superposition principle will not hold. So what will be be the general solution? The degree of equation is one.