When using Laplace transform to solve the IVP Uz =Ux; - o 0 u(x,0) = x. then e[u]= а. -Sx e S -sx - - - b. 1 S С. 1 -Sx – c e Sx -Sx e S + s2 X e SX - - s2 е. -sx e s2 1 SX s2 g. - - s2 1 -Sx. e h. -Sx e S sx – c e $X - + d. f.

Q: Activity 5.6 1. Obtain the general solution of the given ODE on (0,00). (a) x²y" + xy + (x² - ) y =…

A: The given Ordinary differential equation is: on .To find: The general solution for the given…

Q: 2. Start: y= x What transformations occurred? End: y =-9(x-8)² + 5

A: First   shift the graph right by 8 units.  Then  strecth by (-9) units.  Then  shift upward by 5…

Q: Let X₁ and X₂ have the joint pdf fx₁,x₂(x₁, x₂) = 10x₁x² for 0 < x₁ < x₂ < 1, and 0 elsewhere.…

A: Given pdf  f(x1,x2/=10x1x22 0&lt;x1&lt;x2&lt;1

Q: 7. Using Lyapunov functions, show that the origin is unstable for the ODE i = -x3 ÿ = -y3

A: The solution is given below

Q: L[2t2 + 5 – 3 cos nt), t > 0

A: We use the Linearity property and table of Laplace transform to find the answer of the given…

Q: * (). Partial Differentiation. If u = In(x² + y²) and z = sin-1 evaluate the following: a²u 1. əx2

A:

Q: The finite difference approximation of the first derivative in the explicit method used to solve…

A: For the first derivative .

Q: , solve this D using the differential operator (D - 13D2 + 36)y = 2e2x + 3e-2x + 4e3x + 5e-3x + 10e*

A: Using method of undetermined coefficients

Q: Which functions form the basis of solutions for the ODE y – y" – y" +y' (x) = 0? O {1, e ?, e², æe }…

A:

Q: Let X (0,1). Derive the characteristic function of Y-X².

A: Y = X^2, where X is a random variable with a standard normal distribution (mean 0 and standard…

Q: Example F Taking the z-transform of each term of the second-order equation Yk+2 +a1Yk+1+a2Yk = Rk…

A: Let us consider the second order inhomogeneous difference equation  yk+2+a1yk+1+a2yk=Rk…

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

A:

Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

A:

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

A:

Q: different directions and the (x-1) If 4 7 (x-)? If y =(x-1)2 • Determine f is contincous in (1,0)…

A:

Q: +. + 1 3. Exer. 33-36: Use right-hand and left-hand derivatives to prove that f is not…

A:

Q: The graph of the function below intersects at t axis on the interval [0, 4rt] at points f(t) = cos t…

A: We know that f(t) = cos(t) It cuts the t axis at the points π2,0 , 3π2 , 0 , 5π2 , 0 , ...

Q: Q4. (a) Give A = 2xy â, +3â, +z'yâ,, calculate v.AdV as shown in Figure Q4(a). A, (0, 1, 1) (0,0, 1)…

A:

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

A:

Q: The function y = (x- 1)(x-2)(x - 3) is negative on the interval(s) %3D O a) xe (-0, 1) and x e (2,…

A: We have y=x-1x-2x-3 First, we find the critical points by letting y=0: y=0⇒x-1x-2x-3=0⇒x-1=0, x-2=0,…

Q: Discuss the continuity of the function 2ху +y? f(x.y): (x, y) # (0,0)

A:

Q: (x + 3)³ 12 16 11 f(x) Consider the function 4(х — 1)2 4 1 (x – 1)2 4. Note that - (x – 9)(x + 3)²…

A:

Q: v=e2r-y cos (y– 2x) Obtain the value of of the relation дхду A 8e2r-y sin (y– 2x) B - 6e2 -y cos(y–…

A: Option (C) is the correct.To solve this question first we take the partial derivative with respect…

Q: f(2) — и(х, у) + jo(x, y) и(х, у) — е% сos x — х f (0) = 1

A:

Q: Solve for the inverse Laplace Transform of 8 F(s) 53 - 3s2 – 4s 8 f(t) = – 2t + 2 a. + te4t Ob. 8…

A:

Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: 26. Evaluate the gradint of f (x,y,₁z) = log (= ² + y² +₂²) at (1₁91)-11

A:

Q: Integral Representation r(c) Г(В)Г(c-b) Jo -2 F₁ (a, b; c; x) = for F, : ¹ (1 - ₁)¤-b-¹ (1-x₁)¯ª di…

A:

Q: ди t. + 2x Ət ди ?x - 1, -∞ 1,

A:

Q: Determine the inverse Z-transform of X(z) Select one: akt xk = = (-2j) sin( 2 (2a)k-1 sin (47) 2 xk…

A: Inverse Z transform of the function

Q: успЈ where /_g[n_1] + n[n] 2 x[n] = (!) u[n]

A:

Q: find the Inverse Laplace Transform 4s + 5 (s 1)² (s+2)

A: Solution :  Options (iv) is correct

Q: 8. (p.241, #4) The function f: R → (0, 0) defined by f (x) = e**+1 is bijective. Find its inverse.

A: Replace f(x) with y.

Q: Learning Target Ol: I can use propositional variables and logical connectives to represent…

A: The given statements,: It's over degrees.: It's too hot.: I will bike today.The aim is to find the…

Q: (2) The derivative of r at the попzеrо real nuтвer a is Dr.(h) = -h/a². Proof. (1) Compute, p(a + h,…

A:

Q: Find the singular points of the ODE and determine if each singular point is regular or irregular. a.…

A: