solve the given de or ivp 3. [2xy cos (x²y) - sin x) dx + rcos (2²y) dy = 0.
1. cos 4 x-sinº x = cos 2x 6 6 2. sin x + COS x = 1-3sin ?x cos” x 3. cos 2x = 1-tanx 1+tanx 4. 2sinx cosx = cos(x-y) – cos (x+y)
8. 2 sinº x-3 sin x-1=0 11. 4 sin’ x + 7 sin x = 6 9. tanx-1=0 12. ( tan x-)(tan x-3) = 0
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...
SOLVE #3 AND #4 PLEASE Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0 Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
Solve each differential equation. (Don't use the Laplace transform. 3. IVP: y + cos(x + y) + (x – y + cos(x + y)) = 0, y(0) = 7. If the equation is exact equation, then solve it. If not, find only an exact equation.
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m. Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
5. 2 cos x cos y= cos(x+y) + cos (x-y) 6. sin2x + sin 2y = 2 sin(x+y)cos(x-y)
(1 point) Solve the following differential equation: (tan(x) 8 sin(x) sin(y))dx + 8 cos(2) cos(y)dy = 0. = constant. help (formulas)