Consider the linear second-order differential equation:

d^2y/ dx^2 + a1(x)dy/dx +ao(x)y(x)=0

Note that this equation is linear because y(x) and its derivatives appear only to the first power and there are no cross terms. It does not have constant coefficients, however, and there is no general, simple method for solving it like there is if the coefficients were constants. In fact, each equation of this type must be treated more or less individually. Nevertheless, because it is linear, we must have that if y1(x) and y2(x) are any two solutions, then a linear combination.

y(x)=c1y1(x)+c2y2(x) where c1 and c2 are constants, is also a solution. Prove that y(x) is a solution.