Consider the nonhomogeneous differential
equationy"-2y'-3y=2(e^(
find a paricular solution to the non homogeneous equation.
also write the general solutiong to the
nonhomogeneousequation.

Step-by-step explanation:

For homogeneous solution:

So since roots are r = 3 and r = -1,

Since we are given , we will use undetermined coefficients. However, here the trick is we have in homogeneous solution. So in particular solution, as undetermined coefficients, we will use instead of .

Hence,

So,

Hence,

General solution is:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.