Particular Solution of a Nonhomogeneous Linear Second-Order Differential Equation with Constant Coefficients

This Demonstration shows the method of undetermined coefficients for a nonhomogeneous differential equation of the form with , , , and constants. If , then the form of the particular solution is . If and , the particular solution is of the form . If and , the particular solution is of the form .

The second part shows the solution of a linear nonhomogeneous second-order differential equation of the form . Let be a root of the corresponding characteristic equation. If , the particular solution is of the form . If and , the form is . If has multiplicity 2, then is a real number and the form of particular solution is .

The general solution of a nonhomogeneous linear differential equation is , where is the general solution of the corresponding homogeneous equation and is a particular solution of the first equation.

Reference

[1] V. P. Minorsky, Problems in Higher Mathematics, Moscow: Mir Publishers, 1975 pp. 262-263.