1 point) Check by differentiation that y 3 cos 2t+3 sin 2t is a solution to...
Use variation of parameters to find a particular solution to the given DE -3pt 11.)y" - 2y'+y- tet 13.) y'', + 4y'--8 [cos (2t) + sin(2t)] 15.) хту-xy' + y = x3 6e
Use variation of parameters to find a particular solution to the given DE -3pt 11.)y" - 2y'+y- tet 13.) y'', + 4y'--8 [cos (2t) + sin(2t)] 15.) хту-xy' + y = x3 6e
(1 point) Find the solution of y" + 4y' = 256 sin(41) + 160 cos(4t) with y(0) = 4 and y'(0) = 4.
The solution of the initial value problem y" + 4y = g(t); y(0) = -1, y'(0) = 4 is ОВ. cos 2t y = į SÓ 9(T) sin 2(t – 7)dt + 2 sin 2t – cos 2t y = {G(s) sin 2t + 2 sin 2t y = So 9(7) sin 2(t – 7)dt + 2 sin 2t – į cos 2t y = £g(t) sin 2t + 2 sin 2t – } oc OD COS 2t OE y...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
(1 point) Find a particular solution for each differential equation y" + 3y = 5t, then yp = y" - y = 3et sin(t), then yp = y" + 4y = cos(2t), then yp =
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
1. Find the general solution to the equation y" - y - 2y = -e- 2. Find a particular solution to y" + 4y = 11 sin(2t) + cos(2t) 3. Find the form of a particular solution to be used in the Method of Undetermined Coefficients for the equation y" + 2y' +2y = te-* cost Do not solve the equation
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
(1 point) Given the acceleration vector a(t) = (-4 cos (2t))i + (-4 sin (2t))j + (-3t) k , an initial velocity of v (0) =i+ k, and an initial position of r (0)=i+j+ k, compute: A. The velocity vector v (t) = j+ . B. The position vector r(t) = j+ k