If ar2 + br + c = 0 has equal roots r1, show that L[ert] = a(ert)" + b(crt)' + cert = a(r - r1 )2er1. Since the right side of is zero when r = r1, it follows that exp(r1,t) is a solution of L[y] = ay" + by' + cy = 0. Differentiate with respect to r and interchange differentiation with respect to r and with respect to t, thus showing that Since the right side of is zero when r = r1 conclude that t exp(r1 t) is also a solution of L[V] =0. Determine a suitable form of Y(t) if the method of undetermined coefficients is to be used. y" + 2y' + 5y = 3et-t cos2t - 2te-2t cost

Solution is in the following attachment.

Step-by-step explanation:

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: