nsider the differential equation y" - 3y + 2y = 5t². (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11, 12 = 1,2 (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. y₁ (t) Y₂ (t) = exp(t) = exp(2t) (c) Find a particular solution y of the differential equation above. yp (t) Σ M M M

Q: what is csc(alpha+beta)=?

A: Given that the trigonometric functioncscα+β

Q: Solve the initial value problem below using the method of Laplace transforms. y" - y = 5t-10e¯t,…

A: The given initial value problem is        y" - y = 5t - 10e-t . . . . . (1)        y(0) = 0 , y'(0)…

Q: Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the…

A: Given, The temperature varies between 73 and 87 degrees during the day. The average daily…

Q: Consider the following double integral: 1 1 √y cos(y) dy dx x² If you need to use any theorems…

A:

Q: Q) The Sum of three numbers is 6 If we multiply the third numbers by 2 and add the first number to…

A:

Q: + tany)dx + xsec³ydy 4) Evaluate (¹ Y=X²-1 from (1,0) to (2, 3) where C is the curve

A:

Q: | Let ƒ(x, y) = 4x² + 7xy + 4y² + 7x − 7y + 4. Find the linearization L(x, y) of f(x, y) at the…

A:

Q: (D^3-2D^2-5D+6)y=e^(3x)

A:

Q: The solutions of initial value problems for linear first order differential equations are defined on…

A:

Q: Determine the inverse Laplace transform of the function below. S-3 3s² + s +9 Click here to view the…

A:

Q: . The helix curve is 3 a(t) = (cost, 2 sint, 3). (a) Find the tangent vector T. (b) Find the normal…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. w" - 6w' +9w=18t+ 78,…

A:

Q: Find a parametric representation for the surface. the plane that passes through the point (0,-1, 4)…

A: Note:  "As per your requirement, I answered here both the questions."   Given,  The plane that…

Q: Problem: Using the language of differential forms, find the value of the integral of the vector…

A: Here, we need to find the integral of the vector field          A=2+z2∂x+y2∂y+2xz∂z along the curve…

Q: Determine all the primes p such that p^2 77 has exactly 5 positive divisors.

A:

Q: Parametrize this surface. Calculate the flux of the vector field F(x,y,z)=(xy,xz,zx) through the…

A: As per the question we are given the following surface : S : z = x sin(y) , 0≤x≤2 , 0≤y≤π And the…

Q: Consider the curve with parametrization given by: r(t) = (-4 cost, 4 sint, 8t) Now re-parametrize…

A: Given Data: Let us consider the given curve with parametrization given by, rt =-4 cost ,4 sint , 8t…

Q: Prove that x''' + yul + zm2 = where dashes denote differentiation w.r.t.s. 1 22 + 1 + p" p* -176 402

A:

Q: What can we say about 5"-2" for any natural number n? Justify your response. which 15 divisible by 3

A: For n = 1,       5n - 2n = 51 - 21                   = 5 - 2 = 3 = 3.1 For n = 2,      5n - 2n = 52…

Q: 59-66. Definite integrals from graphs The figure shows the areas of regions bounded by the graph of…

A:

Q: Let z₁ = 10 + 6i and z₂ = 4 + 6i. Then prove that all the π complex numbers satisfying arg (2) 4 -…

A: The given problem is to prove that for all the complex numbers arg((z-z1)/(z-z2))=π/4  that also…

Q: Let R = Z[i]. show that FR= {r+si | r,sE Q } = Q[i] F a field, Z the integers, Q the rational…

A:

Q: Given the differential equation: Choose all correct answers. A (x²-1) y" - 6x y¹ + 12y=0 D The…

A:

Q: f(x, y) = 6 -√√3x² + 1y² Local maxima are Local minima are Saddle points are m m

A: The given problem is to find the local maxima, local minima and saddle points for the given function…

Q: 13. Find the line pass through two points (1, 2, 3) and (1,0, -1). You should list three different…

A:

Q: 4. Solve absolute value inequalities. Write your final answer in interval notation. a. |-x+ 2-3 ≤ 4

A:

Q: 4x² - 5y = 34, (√6, −2) Tangent line is 6ху = −72, (−2,6) Tangent line is

A:

Q: - The helix curve is (d) Find the torsion 7. 3 a(t) = (cost, sint, 2). 2 (e) Find the curvature k.

A:

Q: ifials

A: We can find how much the point move vertically.

Q: Consider an electron m moving along the line L: (x-3)/2=(y+1)/(-2)=z-1. At L As shown in figure. (A)…

A: We will use vector form of line to find  shortest distance of line from origin . Also we can find…

Q: . Consider the chemical reaction KOH+yH3PO4 → zK3PO4 + wH₂O, in the unknowns x, y, z, w. The number…

A: (a) number of atoms of K in the LHS = x       number of atoms of K in the RHS = 3z…

Q: ' // F F. ds for the given vector field F and the oriented surface S. In other words, find the flux…

A: The given problem is to evaluate the given surface integral over the surface S is the part of the…

Q: Let S be a triangular surface in R³ with vertices at (4,0,0), (0,2,0) and (0,0,8), that is equipped…

A: Flux of a vector field F across surface S  ∫∫SF.dS=∫∫DF.n dA where n is vector normal to the surface…

Q: Find an invertible matrix P and a diagonal matrix D such that P¹AP=D. -7 0 -5 A 18 0 18 = 10 0 8 P =…

A: First we will find out eigenvalues and corresponding eigen vectors of the matrix A.

Q: 3) Solve the following boundary-value problems. a) y'(x) + 2y(x) = 0; y(0) = 0; y' (2л) = 0.

A: The given problem is to solve the given boundary value problem with given boundary conditions.

Q: 10) Consider the following election with five candidates and 21 voters. a) Use the Hare System to…

A: Hare System: Firstly find the majority and tally the 1st place votes. The candidate is declared a…

Q: = function given by llowing heat equation. du at 0x² 1₁ f(x) = X₂ if 0 ≤ 2-x, if1< u(0, 1) = u(2, 1)…

A:

Q: Identify four significant critiques of this chart. Draw on class instruction/discussion on…

A: Given : Chart published in a professional report on state government spending.   To solve : four…

Q: pb4 solve the wave equation BU - 2² (2+2) d²² In a rectangle region 0<x<L, o<Y<H with boundary Ko₁y₁…

A:

Q: Packaging Find the dimensions of an open rectangular box of maximum volume and having an area of 108…

A:

Q: X1 x3 = 0 = 1 3x₁ + x₂ + x3 = −x₁ + x₂ + 2x3 = 2

A:

Q: Solve by homogenous differential equation and the solution in explicit function form y= f(x,y) (8)…

A:

Q: Bobby likes to hike the trails near his house. On Saturday, he spent 4 hours hiking 8 miles. On…

A: We want to find  number of hours spend by Bobby to hiking the trails on Sunday.

Q: 11:2 +¸µ¹¹:¹² + z ¹¹12 Prove that x12 denote differentiation w.r.t.s. = 1 p² 0² + 1+p²². 04 11 1 R²…

A:

Q: 4. Suppose that the square matrix A has a negative eigenvalue. Show that the linear system x = Ax…

A: As per the question we are given a square matrix A having atleast one negative eigenvalue. And we…

Q: A curve is drawn on a sphere of radius a and the principal normal at a point P makes an angle 0 with…

A:

Q: Ex: The average daytime temperature of a city is given by function D(t) = 5cos(301) 20⁰ where t is…

A: Given, The average daytime temperature of a city is given by the function D(t) = 5cos(30t)°+20°…

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A:

Q: A dosage chart tell you to take 1 3/4 mL of liquid medicine. You use this medicine once per day for…

A: On one day, the amount of medicine taken is 134=4+34=74 mL of liquid medicine. This medicine is…

Q: The Truly Amazing Dudes are a group of comic acrobats. The weights (in pounds) of the ten acrobats…

A: Given sample consists of 10 data points. Sample mean and deviation are 154.4 and 31.1 respectively.…