3. Classify the following PDE as (i) Linear or Nonlinear, (i) Homogeneous or nonhomogeneous а. х ихх — у иуу = 4 a²u b. (x – 1): ax2 au = cos X ax C. -2 uxx + uxy + 4uyy +5 uz +5u = 0 %3D

Q: 3. For the competing species population model dx —D х(-х — Зу + 150) dt dy %3D У(-2х — у + 100) dt…

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Q: 4. Determine when the following pairs of functions are linearly independent. (a) yı(t) = erit; y(t)…

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Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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Q: Convert the following 2nd order IVP to a 1st order system IVP, by viewing y' as a second dependent…

A: Given: We have to convert the given 2nd order IVP to a 1st order system IVP, by viewing  as a second…

Q: 6. For what values of y(0) will the solution of y' = y(y – 2),x > 0 a) be a constant function b) be…

A: First of all we draw the direction field of the differential equation y' = y(y-2)

Q: we considered the Position Servo described by the state equation where A = T x(t) = Ax(t) bu(t) + IT…

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Q: The D.E. of the cubics cy² = x²(x − a) with “a” held fixed is a. y(3x - 2a) = 2x (x -a)y' (a). c.…

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Q: 6. A mass-spring-damper system has the equation ma" + ßx' + kx = F(t), where r(t) is th displacement…

A: Given , mass-spring-damper system equation as- mx''+βx'+kx=Ft To find the units of β and k in the…

Q: 1) A circular cylinder with radius r cm and heigh (a) Compute V(2, 5). (b) Find the linear…

A: Given: To explain the given statement as follows, Volume V =π r2h cm3

Q: 1. Let XU(-2, +), i.e. E x [1, € (-+) otherwise fx(x) = { 0, Determine the pdf, fy (y), of Y, where…

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Q: a) z = 4x²y-sen(3x - 4y)

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Let f(x, y) = x³ + y³ - 2x²y². Calculate fa, fy, fax, fyy and fry. Hence show that (3/4, 3/4) is a…

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Q: Given that u. = = = , show that EE,(tB)ij = 0, where (tB)ij is the interaction effect in the…

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Q: dy 1. FIND BY IMPLICIT DIFFERENTIATION: 9x = secy dx dy 2 a) FIND BY IMPLICIT DIFFERENTIATION: x4y³…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose that the gravitational force is not give by the inverse-square law, and instead is F grav =…

A: Step 1: Step 2:Step 3: Step 4:

Q: (Exercise 3.4.104) a) Find the general solution of x' = y,y' = -x. b) Sketch the phase portrait,…

A: Given: x'=y.y'=-x The given points are (1,0) and (3,0)

Q: = x³y² – 3x²y + 5x – 3y + 12

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Q: 1. a) The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while the height, h, is…

A: The diameter of a balloon, d, is decreasing at the rate of 0.3 cm/s while the height,h, is…

Q: 1. Find the differentiation of the following functions with respect to x I. y = Jx3 + 5x – 7) II. y…

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Q: Write down the equation of motion for the point particle of mass m moving in the Kepler potential…

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Q: (3) Consider the derivative: 2xydx + (x² + 2y)dy. Evaluate whether this is a total derivative or an…

A: We will check whether the given function is total derivative or not. Consider dz = (2xy)dx + (x 2 +…

Q: Thus, for u = g(x) = sin(5x), %3! f'(g(x)) = F'(sin(5x)) = 8 %3D %3D 8 Next we calculate g'(x). g(x)…

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Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: 1. A tract of land has a trapezoidal shape with two parallel sides a and b and the distance between…

A: The solution is given below: Given a=125.42 m, b=208.84 m, h=44.99 m