Find the solution of the following nonhomogeneous linear system y1′ = y2 + 1 , y2′...

Find the solution of the following nonhomogeneous linear system

y₁′ = y₂ + 1 ,

y₂′ =−y₁ + t.

Expert Solution

We solve the given system of nonhomogeous equations.

milcah answered 2 years ago

a) verify that y1 and y2 are fundamental solutions b) find the general solution for the...

a) verify that y1 and y2 are fundamental solutions b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation 1. y'' + y' = 0; y1 = 1 y2 = e^-x; y(0) = -2 y'(0) = 8 2. x^2y'' - xy' + y = 0; y1 = x y2 = xlnx; y(1) = 7 y'(1) = 2

Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x)...

Problem 3: Find a second solution by reduction of order - nonhomogeneous The given function y1(x) is a solution of the associated homogeneous equation. Use the reduction of order method to ﬁnd a solution y(x) = u(x)y1(x) of the nonhomogeneous equation. 1. x^2y'' + xy'−4y = x^3, y1 = x^2 2. 2x^2*y'' + 3xy'−y = 1/x , y1 = x^(1/2)

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).

Let c(y1, y2) = y1 + y2 + (y1y2)^ −(1/3). Does this cost function have economies...

Let c(y1, y2) = y1 + y2 + (y1y2)^ −(1/3). Does this cost function have economies of scale for y1? What about economies of scope for any strictly positive y1 and y2. Hint, economies of scope exist if for a positive set of y1 and y2, c(y1, y2) < c(y1, 0) + c(0, y2). [Hint: Be very careful to handle the case of y2 = 0 separately.]

Use the simplex method to solve the following problem. Find y1 ≥ 0, y2 ≥ 0,...

Use the simplex method to solve the following problem. Find y1 ≥ 0, y2 ≥ 0, and y3 ≥ 0 such that 2 y1 + 7 y2 + 3 y3 ≤ 11, 2 y1 + 14 y2 + 8 y3 ≥ 1010, and w = 12 y1 + 42 y2 + 59 y3 is minimized. The minimum value w = ___ occurs when y1 = ___, y2 = ___, and y3 = ___. (Simplify your answers.)

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤...

The joint density of Y1, Y2 is given by f(y) = k, −1 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, y1 + y2 ≤ 1, y1 − y2 ≥ −1, 0, otherwise a. Find the value of k that makes this a probability density function. b. Find the probabilities P(Y2 ≤ 1/2) and P(Y1 ≥ −1/2, Y2 ≤ 1/2 c. Find the marginal distributions of Y1 and of Y2. d. Determine if Y1 and Y2 are independent e....

a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential...

a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential equation b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation y'' - y = 0 y1 = e^x, y2 = e^-x : y(0) = 0, y'(0) = 5

Suppose that Y1 and Y2 are jointly distributed with joint pdf: f(y1,y2) ={cy2. for 0 ≤...

Suppose that Y1 and Y2 are jointly distributed with joint pdf: f(y1,y2) ={cy2. for 0 ≤ y1 ≤ y2 ≤ 1 0. otherwise} (1) Find c value. (2) Are Y1 and Y2 independent? Justify your answer. (3) ComputeCov(Y1,Y2). (4) Find the conditional density of Y1 given Y2=y2. (5) Using (d), find the conditional expectation E (Y1|Y2). (6) Suppose that X1=Y1+Y2, and X2= 2Y2. What is the joint density ofX1andX2?

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2...

Suppose that Y1 and Y2 are random variables with joint pdf given by f(y1,y2) = ky1y2 ; 0 < y1 <y2 <1, where k is a constant equal to 8. a) Find the conditional expected value and variance of Y1 given Y2=y2. b) Are Y1 and Y2 independent? Justify your answer. c) Find the covariance and correlation between Y1 and Y2. d) Find the expected value and variance of Y1+Y2.

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z....

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z. Show that the relation∼is an equivalence relation and describe the equivalence class of the point (0,1).

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