Find G. y" - 4y' + 3y = 3x^2 - 2x - 3. H. y" - 4y' + 3y = 9x^2 I. y' - 4y = 2e^2x J. y' -4y =...

Question:

Non-Homogeneous Second Order Differential Equation:

To solve a non-homogeneous linear differential equation of second order with constant coefficients,

{eq}a\frac {\partial^2 y}{\partial x^2} +b\frac {\partial y}{\partial x} +cy =g(x)\\ a \,\,\, b \,\,\, c \,\,\,\, \textrm {constants}\\ {/eq}

we must look for the complementary solution {eq}y_c {/eq} and find the particular solution {eq}y_p {/eq} of the non-homogeneous equation.

Then, the general solution is: {eq}y = y_c + y_p {/eq}

One of the methods to find the particular solution is that of undetermined coefficients. This method is used when g (x) has a special form, involving only polynomials, exponentials, sines and cosines, or g (x) is a finite linear combination of this functions.

The method is called the undetermined coefficients method because it is a coherent proposal about the form of the particular solution.

Answer and Explanation: 1