d^2y/dx^2 +p(x)dy/dx +g(x)y=r(x), then the quadratic form of the differiential equation: r^2+p(x)r+g(x)=0,then use quadratic formula or factor to get roots or imaginery roots. Then use the equations: c_1*e^r_1x+c_2*e^r_2x or e^ax(c_1*cos(bx)+c_2*sin(bx) to get general solution.