Find the length of the curve. r(t) = cos(3t) i + sin(3t) j + 3 ln cos t k, 0 ≤ t ≤ π/4

Question: Calculate t * cos(3t), where * denotes convolution. t*cos(3t) Show transcribed image text.

Question: Use the Laplace transform method to solve the following initial value problems1. x" -x' -2x = 0 x(0) = 0 and x'(0)=22. x" + 8x' + 15 = 0 with x(0)=2 and x ...

Answer: y(t) = 2etcos(3t) - (7/3)et sin(3t) - sin(3t) (Please show all work so that I can learn this) Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Question: Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed.

And then, find when cos is -1/2 (x value from x,y) : 2π/3 and 4π/3.

Solve the following initial value problems:(a) y''+2y'+y=cos(3t),y(0)=1,y'(0)=1(b) y''+5y'+6y=t+e-2t,y(0)=-1,y'(0)=2 Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Find the general solution of the differential equation (d^2x)/(dt^2) + 9x = cos(3t) Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.

Consider the initial value problem y" + 9y = cos (3t), y(0) = 5, y'(0) = 9. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(y) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below).

Find the amplitude (exact number) and phase angle (8, rounded to the nearest hundredth of a radian) of the steady-state solution of the system ö + + x = 4 cos 3t. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on.