How To Solve A Second Order Homogeneous Differential Equation. Otherwise, the equation is nonhomogeneous (or inhomogeneous). This tutorial deals with the solution of second order linear o.d.e.’s with constant coefficients (a, b and c), i.e.

Y = ert (a cost+ b sint). 2(x) are any two (linearly independent) solutions of a linear, homogeneous second order differential equation then the general solution y cf(x), is y cf(x) = ay 1(x)+by 2(x) where a, b are constants. Let the general solution of a second order homogeneous differential equation be \[{y_0}\left( x \right) = {c_1}{y_1}\left( x \right) + {c_2}{y_2}\left( x \right).\] instead of the constants \({c_1}\) and \({c_2}\) we will consider arbitrary functions \({c_1}\left( x \right)\) and \({c_2}\left( x.