Question

For the differential equation: d^3y/dx^3 - 3 d^2y/dx^2 + 4y = 3x + 1, which of the following statements is incorrect? Its complementary function is y_c = (c_1 + c_2x) e^{2x} + c_3e^{-x} where c_1, c_2 and c_3 are real constants. The auxiliary (characteristic) equation of this differential equation is lambda^3 - 3lambda^2 + 4 = 0. This differential equation can be written as (D^3 - 3D^2 + 4) y = 3x + 1. The form of a particular solution for this differential equation is Ax+B where A and B are real constants. This is a third-order nonhomogeneous linear differential equation with constant coefficients.

          For the differential equation:
d^3y/dx^3 - 3 d^2y/dx^2 + 4y = 3x + 1,
which of the following statements is incorrect?
Its complementary function is y_c = (c_1 + c_2x) e^{2x} + c_3e^{-x} where c_1, c_2 and c_3 are real constants.
The auxiliary (characteristic) equation of this differential equation is lambda^3 - 3lambda^2 + 4 = 0.
This differential equation can be written as (D^3 - 3D^2 + 4) y = 3x + 1.
The form of a particular solution for this differential equation is Ax+B where A and B are real constants.
This is a third-order nonhomogeneous linear differential equation with constant coefficients.

For the differential equation:
d^3y/dx^3 - 3 d^2y/dx^2 + 4y = 3x + 1,
which of the following statements is incorrect?
Its complementary function is yc = (c1 + c2x) e^2x + c3e^-x where c1, c2 and c3 are real constants.
The auxiliary (characteristic) equation of this differential equation is lambda^3 - 3lambda^2 + 4 = 0.
This differential equation can be written as (D^3 - 3D^2 + 4) y = 3x + 1.
The form of a particular solution for this differential equation is Ax+B where A and B are real constants.
This is a third-order nonhomogeneous linear differential equation with constant coefficients.

Added by William D.

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