I read a theorem on second order differential equations which said that:
"If y1 and y2 are linearly independent solutions of a differential equation which is of the form a(Dy2) + b(Dy) + cy = 0 (homogeneous), and a is never 0, then the general solution is given by
y = c1*y1 + c2*y2
where c1 and c2 are arbitrary constants"
My question is, if we already have two "linearly independent solutions", why do we need to find this third solution? Is it necessary?
Thanks in advance!