Let Y1(x) Y2(x) be two linearly independent solutions of the homogeneous equation y''+p(x)y'+q(x)y=0. Select all of the correct statements for the two-point boundary value problem

y''+p(x)y'+q(x)y=g(x)

y(0)=y0,

y'(L)=yL'

When this two-point boundary value problem has no solution, the corresponding homogeneous equation also has no solution.

When the matrix A =

Y1(0) Y2(0)
Y1(L) Y2(L)
is invertible, the nonhomogeneous two point value problem has a unique solution for any choices of g(x), y0, yL'

When this two-point boundary value problem has infinite many solutions, the corresponding homogeneous equation also has infinite many solutions.

This two-point boundary value problem could have no solution when the corresponding homogeneous equation has non trivial solutions.

The corresponding homogeneous equation is obtained by setting g(x)=0, y0=0, yL'=0

answer: for each 3 girls there is 2 boys . 3: 2

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when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

144.50

step-by-step explanation:

21.5 x 13.4=288.10 divide by 2

step-by-step explanation:

yes it represnts a functio, their are not 2 of the same numbers on the both sides