2. a) Solve the differential equation: 2²/" - 6xy' = 27 6 Oy=4 +6226 + Ins 6 36 Oy=c+ c2 26 76 36 + In 3 6 6 27 Oy=4+ c227 + In 7 ...7 49 Oy=q+cqz? 27 In 2 49 +7 None of the above b) Solve the differential equation: 9z+y" + 9xy' +25y = 0 Oy= cos(5 ln /3) + sin(5 In 3/3) Oy=425 +2.23 Oy=C1 cos(52/3) + 2 sin(5x/3) y=4125 + c2205 in None of the above...
2y, and y = 8 when t=0. Solve the equation. O y= 228 Oy=est Oy - det
(a) i) For ∫(4x−4)(2x^2-4x+2)^4 dx (upper boundry =1, lower =0) Make the substitution u=2x^2−4x+2, and write the integrand as a function of u, ∫(4x−4)(2x^2−4x+2)^4 dx =∫ and hence solve the integral as a function of u, and then find the exact value of the definite integral. ii) Make the substitution u=e^(3x)/6, and write the integrand as a function of u. ∫ e^(3x)dx/36+e^(6x)=∫ Hence solve the integral as a function of u, including a constant of integration c, and then write...
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need mechanisms explained thanks
???? ОН OH racemic 1) Na 0&+/E+0H 2 km n Oy Nadh cold (or Os04) ???? racemie E-Alkene 1) kM noy NaOH.cold (or 0504) 해 (syn add. of Diols'
l. Find the general solution: (a) r" -4x +4x-0 (b) "-2r (c) 0. (d)4r' +3r-0
DP, Wary i wię In ozeigenvector basis, we have oy = with eigenvalues = +1 and eigenvectors = 1 Fil G). Find the transformation matrix to transform from ozeigenvector basis to oyeigenvector basis. Then use it to find the representation of the Oy eigenvectors and oy in the new basis. Discuss is this expected?
3x +2 <0 and 4x -320
8. Let Y, Z be uncorrelated with My = uz = 0 and oy = ož = 02, and let X(t) = Zcos(t) + Ysin(t). In class, we showed that X() is WSS. Now let fy = fz where fz is as shown below. Afz(2) 1/2t 1 2 a) Show that My = Uz = 0. b) Find oy = oz. c) Find fx(x;0). d) Find fx(x;). e) Show that X() is not 1st order stationary. Note that you have...
14. Find the center, vertices and foci of the ellipse. Sketch the ellipse. a. 9x24y2 = 36 b. Cx-2)2 Cy+3)2 + = 1 25 16 C. 2x2y= 2 + 4x - 4y
14. Find the center, vertices and foci of the ellipse. Sketch the ellipse. a. 9x24y2 = 36 b. Cx-2)2 Cy+3)2 + = 1 25 16 C. 2x2y= 2 + 4x - 4y
Which of the following is of the form of a non-homogeneous second-order linear DE? OR(Cy" + P(Zy' +Q(2y = f(2) O P(1)y' +Q(I)y = 0 OR(Cy" + P(2)y' +Q(I)y=0 O none of the other options O P(x)y' +Q(z)y = f(x)