4. Determine when the following pairs of functions are linearly independent. (a) yı(t) = erit; y(t) = er²t, r₁,72 € R (b) y(t) = cos(at); 32(t) = sin(at), a = R (c) y₁ (t) = cosh(at); y₂(t) = sinh(at), a € R

Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

A:

Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

A:

Q: Find the derivative of y with respect to s. y= sec 1(7s° + 4)

A:

Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

A:

Q: Find y as a function of t if 16y" + 16y + 4y = 0, and y(1) = 2, y'(1) = 3. y =

A: The given differential equation  and the initial conditions .The objective is to find the solution…

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: calculate the derivative at t = 3, assuming that rị(3) = (1, 1, 0) , r2(3) = (1, 1, 0) r{ (3) =…

A: To calculate: ddt6r1(t)-4·r2(t) at t=3, where r1(3)=<1,1,0>,…

Q: Consider the curve given by y² = 2 + xy. dy dx (a) Show that = 2y-x (b) Find all points (x, y) on…

A:

Q: (g) Suppose that r₁ (0) =, r₂(0) =, r₁(0) = ar r₂ (0) =. Use this information to evaluate the…

A: We are given:

Q: Find the direction in which the function g(x, y) = cos(xy) decreases fastest at the point (1, pi)

A:

Q: Consider the following function which is defined for all x and y: ƒ(x, y) = 2(1 − p²)x²y² − x² - y²…

A:

Q: 2. Find the first and second derivatives. Simplify as needed. (a) f(t) = t sin t )=-=- (b) h(r):

A: