13 By direct partial integration, Solve the following PDES s. 8²u ахбу = CEX COSysXu(X,t) Ex UCH, y) 20 (#, = 2 Ans: u(x, y) = sinx sing + X/² + 2 cosy - #2²

Q: Evaluate: du [(x²-y²)²1 ³₁ 1² du dt x+y

A: Given , ∫-13∫02x2-y22x+ydudt

Q: ¹₁1+x²x+2y dy dx

A: We need to evaluate the following iterated integral as following: ∫-11∫2x21+x2x+2ydy dx

Q: 2-S Sin ³ x cos" x dx

A: SOLUTION-

Q: 5. I. Evaluate each determinant. -2 -1 4 2 5

A:

Q: 2 ³₁²₁²[z³(x + y)³] dz dy dx -4 J

A: In this question we have to solve the given triple integral.

Q: 10) y7 exbx

A:

Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

A:

Q: Evaluate the line integral y dx + xy dy where C' is the rectangle with vertices (0,0), (5,0), (5,4),…

A:

Q: y=u² +2u u=v² + 2v v = x² + 2x

A:

Q: Given a second order differential equation dx 3t 2x = e³t dt where t = 0, x = -5. Using Laplace…

A:

Q: 4 Find the general Solution of the following PDES • з Их + 2 Иу -Х ucx, c) - че 2 (зу-2х)12 ans3-…

A: To find the general solution of the given PDE .

Q: Find the particular solution of the DE y11 + 24y = 0 subject to the initial conditions y(0) = 2 and…

A:

Q: Find the solution of the given initial value problem. ty+3y=t²t+5, y(1) = 2, t> 0 11

A:

Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π <x<π

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: Solve the given differential equation. All solutions should be found. (5y¹ + 2x³y) dx − (4xy³ + x¹)…

A: Using integrating factor make equation exact

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem for this function f and…

A: This question can be solved using the concept of mean value theorem.

Q: 3 Evaluate: ₂(4x²y - z³) dz dy dx

A:

Q: 5x 2 Evaluate: f fx fdz dy dx 2

A:

Q: Q5/ Solve for x the following inequality and show their solution set (x: x2-x-300)

A:

Q: Given the region R on the right, a. Using vertical strip, SET UP the double integral that will solve…

A: This question is related to double integration, we will solve it using given information.

Q: 2 -1 4 4 -6 1 -3 -5 北

A:

Q: S f(x) dx = [ -6 -5 f -2 Y 7 3 -3 7 X

A: This above given expression of integral is shows integral value of function f(x) from x=3 to x=7.

Q: Evaluate: £²³₂ £²₁ ₁²[z³(x + y)³] dz dy dx

A:

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A:

Q: y ye 2x+4 tax

A:

Q: Evaluate the following √ (2²2 + + 6x − 1)²(x + 3)dx (x²+6x-1)-5 + C 2 (x²+6x-1)-5 3 +C (x²+6x - 1)5…

A: We have to solve given integration.

Q: Evaluate the following [s sin(4x) dx cos(4x)/4 + C -4cos(4x) + C - cos(4x)/4 + C O-4cos(4x) + C

A: To evaluate: Integral

Q: 2 \n'/x/ ax

A: We will solve the problem.

Q: Evaluate: ff xy² dx dy

A:

Q: f) y = x²-1 x²+x-2

A:

Q: Q1 Solve the following differential equations. 1. (x + 1) = x(y² + 1) dy dx

A:

Q: t√√t + ,2 + t dx

A:

Q: 1. Given vector 2 0-3 is 2. It is known that a à vector : ( 2 ) and 3 = (-1) is a vector in 1R³ with…

A:

Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A:

Q: Use Stokes' Theorem to find the circulation of F = 5y + 5zj+2ak around the triangle obtained by…

A: We have to find the circulation of F→.

Q: Solve the following system by Gauss-Jordan elimination. 2x1 + 7x2 + 33x3 = 29 6x122x2 + 105x3 = 91…

A:

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A: Let's solve given diffrential equation by using laplace transform.

Q: Consider a continuous function f(x) = 2e-1-2x, which is true about the relative extrema of f? f has…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Using exact Solution, find the general solution of the following differential equation: (cos2y -…

A:

Q: Solve for x the following inequality and show their solution set {x: x2-x-30≤0}

A:

Q: show that $(x, y, z) = PDE : 2²4 8²4 дуг дуг + 1 2 x² + y² + z² 824 dz² satisfies the

A:

Q: Find the solution of the given initial value problem. 8 y' - 7 y = cos t t-8 Y(T) = 0, t> 0 t y(t) =

A:

Q: Determine y = Yc+yp using Non-homogenous equations: Method of Undetermined Coefficients Given: y" +…

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Q: Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y²-3x2 and the…

A:

Q: Evaluate: ²₁² [(x²-²²] du dt x+y

A: On solving this we will get

Q: Evaluate √x/2 6sinx(cosx+1) do

A:

Q: Which integral represents the area of R? Choose 1 answer: 3π A 16³ (²1 + 2 cos² (0) + 2 cos¹ (0)) de…

A:

Q: Evaluate: ³₁² [(x² - y²) ² x+y 21 du dt

A: The integration of the double integral is  (x2-y2)2/(x+y)

Q: Find the area of the region bounded by the curves 1 y = (x+6)²¹ Y = 4 and the x-axis using vertical…

A: Given problem is :

Q: show that V(x, y) = x 'f (2x+y) is the general Solution of av X du 2X 1 = V ду dax

A: Explanation of the answer is as follows