Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3) Cov(-6X +7, 8Y – 9)

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Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

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Q: Cons i der the linearsystem X2 1. 2. is Gauss-s eidel method

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Q: 11. xy' - y= y23 Answeri: y = (CVx – 1)3

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Q: (b) Find the general solution of d²q dq +60- +50q = 10 cos 2t dt dt² using the method of…

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Q: Solve the nonhomogeneous IVP using the method of undetermined coefficients: y" +4y = x - 2cos 2.x,…

A: To solve the given Homogenous IVP using the method of undetermined coefficients.

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: Solve the fallowing Cauchy problem U4- Au + cu=0 in R" x(0, 0) On IR"x{t=0}. U = where c is a…

A: Given the Cauchy problem as ut-∆u+cu=0,             in ℝn×0,∞                (1) re-write the…

Q: If u(x, t) = D1 fn(t) sin(nx) is the solution Utt – 9ura = 2e2t sin(3x) + e-2t sin(4x) u(0, t) = 0 =…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Given a general antiderivative of x² + 3 +C with initial condition (2, 0), then the particular…

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Q: Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A?…

A: given a matrix A of order 2×2 ,  Av→=3v→ for v→=-1-1 (a) how is the pair 3,v→ called for a matrix A…

Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

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Q: e) y-2y'+y

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Q: 20. Find the general solution to y" + 4y' + 5y = 2e* 1 c. y = e2(cıcos x + c2sin x) -e d. y =…

A: Given that: y''+4y'+5y=2ex

Q: 2nd Case (IBVP Summary) (Ut = 1.5uxx, 0 0 Ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) = 80°F, 0<…

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Q: Find the general solution of the Cauchy-Euler equation: X^3y’’’ - x^2y’’ + 2xy’ - 2y = x^3

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Q: 1. (a) Show that (x) x² is an explicit solution to dy X- = 2y dx on the interval (-∞, ∞). (b) Show…

A: An explicit solution is any solution that is given in the form y=y(x)

Q: 16. Determine the general solution of y" - 2y' + 4y = 4 a. y = e*(c1 cos v3x + c2 sin v3x) + 1 b. y…

A: General solution is CF+PI

Q: If q x2 yz3 %3D =, the small increment in q with &r=8y=8z=±0.1 can be approximately calculated by…

A: We will use partial derivatives to calculate the required quantity.

Q: Find the solution of z'y" + bay + (4 + 4r)y - 0, z > 0 of the form where co 1 Enter n1,2,3,...

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Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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Q: 1. 2xy'+ xy'+ (x² 3) y=O a) Show thet a regulor singulerity Xa>0 is point. 6) Use froteniaw method…

A: (a) Given equation, We know that,

Q: y" – 2y – 2y = 0

A: Given:      y''-2y'-2y=0       -2yx-2ddxyx+d2dx2yx=0 The differential equation has the form:…

Q: 3- Find non-zedo solution ofs dy

A: we need to solve the given first order nonlinear differential equation. The given equation is…

Q: In(x-1) + cos(x-1)% 3 0, Xo = 1.1 %3D %3D I.W: Newton Raphson Method

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Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: 4.Find two solutions (not multiples of each other) of the Bessel equation of order 3232…

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Q: 1. Compute ¡ E px 2 ` y 2 ` z 2 q 1{2 dV , where E “ tpx, y, zq | x ď 0, y ď 0, z ě 0, 4 ď x 2 ` y 2…

A: Use the spherical coordinates to evaluate the integral as follows.

Q: 2 2 x+y e to pday dyd x |-X

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Q: 2. Use substitution to solve the second order y(0)=1 and linear IVP y"-y=0 with y'(0)=0. Hint: Let…

A: Given that, Second order differential equation is, y'' - y = 0…

Q: 7. Use Newtons method with the given X(0) to compute X(2) for each of the following nonlinear…

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Q: SEA 2-Eva luate Edr where Fiy xi)デa C-メ (1-x) } cis por tion of , -1 fn fourth quadrent.

A: We will use Green's Theorem to evaluate the given line integral

Q: Find the general solution of d²y dt² + dy + 20y=e-2t sin(4t).

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Q: 9. Ify,(x)= sin 2r and y, (x) = cos 2x are two solutions of y"+ 4y 0, show that y, (x) and y, r) are…

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Q: #3. Solve the fallowing Caucly problem in R" x(0,0) U4-Ou t cu = 0 u =9 On IR"x{t =0}. where c is a…

A: Given the Cauchy problem as  ut-∆u+cu=0,       in ℝn×0,∞           (1) re-write the equation (1) in…

Q: 1)Show that the forward Euler method applied to the following IVP is stable: y' = 2y – t, y(0) = 1.…

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Q: The solution of the nonhomogeneous DE y" + 4y' +4=5e* is

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Q: Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x=…

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Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: 12. Obtain the general solution of (D4 + 16D² + 63)y = 0 a. y = c,cos v7x + c2sin /7x + c3 cos 3x +…

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Q: The Euler method for approximating a solution to the first order IVP: y' = x + 3y, y(1) = 0 is Yn+1…

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Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

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Q: Find the general solution of the DE y" = xsin(x). O y = -xsin(x) - 2cos(x) + Ax + B y = xsin(x) +…

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Q: 1. E(Y,X, X2... X) (Y+Y2 +. + Yn) 2. E(IX,, X2, X) =E Y2+ + Yp) + -B(X, +X +

A: We have to show that β¯ is conditionally distributed.  To show β¯ conditionally distributed we will…

Q: #3. Solve the fallowing Caucly problem in R" x(0, 0) Uf-Ou t cu =0 on IR"x{t =0}. U = where c is a…

A: