Homogeneous Linear Equations

anxn dny/dxn + an-1xn-1 dn-1y/dxn-1 + ... + a0y = φ(x)
where a0, a1, a2, are constants, is called a homogeneous equation.

To solve put x dy/dx = Dy
x2d2y/dx2 = D(D-1)y
x3d3y/dx3 = D(D-1)(D-2)y
Similarly higher can be substituted.

We get a polynomial to solve.
Solve to find complementary function and particular integral.