Consider the differential equation y'' − y' − 20y = 0. Verify that the functions e−4x and e5x form a fundamental set of solutions of the differential equation on the interval (−[infinity], [infinity]). The functions satisfy the differential equation and are linearly independent since the Wronskian W e−4x, e5x = ≠ 0 for −[infinity] < x < [infinity].

Find the arc length parameter along the given curve from the point where tequals=0 by evaluating the integral s(t)equals=integral from 0 to t startabsolutevalue bold v left parenthesis tau right parenthesis endabsolutevalue d tau∫0tv(τ) dτ. then find the length of the indicated portion of the curve r(t)equals=1010cosine tcost iplus+1010sine tsint jplus+88t k, where 0less than or equals≤tless than or equals≤startfraction pi over 3 endfraction π 3.

What are the possible rational zeros of [tex]f(x) = x^4+2x^3-3x^2-4x+18[/tex]

Point a is located at (0, 4), and point c is located at (−3, 5). find the x value for the point b that is located one fourth the distance from point a to point c. −0.25 −0.5 −0.75 −1