1. y4y+4y=0; yı=e² 2. y" + 2y + y = 0; y₁ = xe¯* 3. y+16y 0; y₁ = cos 4x 4. y9y=0; y₁ = sin 3x 5. yy 0; y₁ cosh x - 6. y" 25y = 0; y₁ = ex 7.9y" 12y' + 4y = 0; y₁ = 23 8. 6yyy 0; y₁ = e3 9. x²y"-7xy' + 16y=0; y₁ = x² 10. x²+2xy-6y=0; y₁ = x² 11. xy" + y'0; y₁ = Inx

0.8 m wo B D E 0.8 m 1.0 m Bar AB rotates about the fixed point A with constant angular velocity wo. The system starts with bar AB horizontal. 1) Use the relative velocity equation to find the velocity of C in terms of the angles 0 and > and their derivatives. 2) Determine the lengths of bars AB and BC so that as bar AB rotates, the collar C moves back and forth between the positions D and E. A design constraint is that bar BC must be longer than bar AB (as shown in sketch). 3) You are given the design constraint that the magnitude of the acceleration of collar C must not exceed 200 m/s². What is the maximum allowable value of wo? 4) Create the following plots for a complete revolution of bar AB using the values for lengths and angular velocity determined above: о о e and > versus time as 2 sub-plots. Position, velocity, and acceleration of C versus time as 3 sub-plots. Velocity and acceleration of C versus its position as 2 sub-plots. - 5) Use your plotted results to describe the…

y On = 0, cos²0 + o, sin²0 + 2 Txy sin 0 cos 0 15.00 Tnt = -(0x - Oy) sin 0 cos 0 + txy( cos²0- sin?0) These equations may also be written as: Ox+Oy On Ox- Oy cos 20 + Txy sin 20 2 8.00 2 Ox- Oy Tnt sin 20 + Txy Cos 20 2 = - 10.00 10.00 55° 8.00 On Both the xyz and ntz coordinate systems are right-handed systems. The z axis is directed 15.00 Tnt toward the viewer. 1st 2nd 3rd Enter solved problems counter attempt

Recharge as follows: Draw the three projection Draw an entire sector O Draw a half of a sector 15 2x020 15 2XR20 20 30 89 45 45 105 015 25 15 50 15

A X₁ RA P₁ X₂ P₂ 2 X3 X L 10 C ХА B RB 22 Z P₁ = 30kN; P₂ = 50kN; w= 10kN/m; L = 6m x₁ = 1m; x₂ = 2m; x3 = 3m; x = 5m Find RA and Rg, and draw SFD and BMD

In Problem 3  use Euler’s method to obtain a four-decimalapproximation of the indicated value. First use h= 0.1 and then useh =0.05. Find an explicit solution for each initial-value problem andthen construct tables similar to Tables 2.6.3 and 2.6.4. 3) y'=y,  y(0)=1;    y(0)

Please solve 509 and 510, thanks!

Which of the following is/are true of the relationship between rotational and linear motion? s = r*9 angular velocity, w, is a vector angular acceleration, a, is a vector. all options a-c are correct only options a-b are correct    2.  Which of the following are true of vector math? a)  The dot product between a vector and itself gives you 0. b)  The dot product between a vector and an exact same vector in the opposite direction gives you -1 . c)  the cross product of a vector with itself gives you 1. d)  the cross product of a vector with the same vector but in the opposite direction gives you -1 .    3.  Which of the following statements are true of tangential and centripetal acceleration? a)  centripetal acceleration can sometimes act in a direction that is away from the center of rotation b)  centripetal acceleration and tangential acceleration are co-dependent on each other c)  the cross product of centripetal and tangential acceleration is 0 d)  centripetal and…

4. Solve the following differential equations: a- y" +zy' ty = x² b- y" -4y = Sinx <- 4"+zy! +y=ex ANS- 9- y = ex (4 x + c₂) +x²-4x+6 2X -2X b- y = Ge²x² + cze²x - is sinx -X C- y=Qe + cake + -X

Please. Answer parts please. Attempt Once. Use cosine and show in rad and degree (2 diff eq)