> Solve the non-exact differential equations (Apply Rule III) 1. (x² + y² + 2x)dx + 2ydy = 0 [Ans. e*(x² + y²) = c ] 2. (x³ - 2y²) dx + 2xydy = 0 [Ans. x + (y²/x²) = c]

Q: √√x-2 (x² − x + 1)² - Q.3 If f(x) = - Find (a) The intervals on which f is increasing, (b) The…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: (a) Determine the Laplace transform of the following expression: te¹ sin 3t

A:

Q: A motion has a equation R (t) = ((₁5 (4+)) 7² + (sm/4+));² The distance traveled by the object in…

A:

Q: Evaluate I = = SSR dx dy where R is the region that lies inside the circle x² + (y-2)² = 4 and…

A: Properties of integration  ∫a2-x2dx=x2a2-x2+a22sin-1xa+c∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx∫cdx=cx+A where…

Q: A string is stretched between points x=0 and x=5. At time t = 0, the elastic medium is at rest and…

A: Given that: A string is stretched between points x=0 and x=5. At a time t=0, the elastic medium is…

Q: 5. Solve for one value of x in x cubed - 8 = 0. a. 1 + 1 sqrt of 3 b. -3 c. -2 d. -1 - sqrt of 3

A: To find- Solve for one value of x in x3 - 8 = 0 1 + i3 -3 -2 -1 - 3   Formula Used-  a3 - b3 = a…

Q: Use the method of undetermined coefficients to determine only the form of a particular solution for…

A:

Q: If W is a subspace of R and v is any vector in R", then ||projwv|+|v-projwv||2= |v||2.

A: Introduction: Every vector that doesn't lie in a subspace can be uniquely expressed as a sum of two…

Q: of R4. Create a basis for U. Consider the subspace X = U = = span{ 2 B 1 08- ‚x}

A:

Q: GIVEN: f(z) = 2z - 5,0 ≤ z < 10 a) Find the FOURIER SERIES of the ODD extension of the given…

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

Q: 13. x = 1 + (y - 2)², x = 2

A:

Q: a. Show that the given differential equation has a regular singular point at x = 0. b. Determine the…

A:

Q: f(x, y) a b) 3xy 4x²+2y² Find the domain of f. Show that the limit = does not exist. lim (x,y) →…

A:

Q: Subject generating function  Let a0 = 1 and an = 2an-1 + 1 for every n >1. Let G(x) be the…

A: Introduction: The generating function is a power series representation of a recurrence relation.…

Q: The following differential equation is an ordinary differential equation. O True O False da 1+1

A:

Q: Evaluate: 3 Sy 21-2² dydz √x² + y²

A: The bounds of x and y are given below x3&lt;y&lt;2x-x2 and 0&lt;x&lt;3/2 y&lt;2x-x2⇒…

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: 4 Given integral is ∫0πsintdt. We have to estimate the given definite integral using the trapezoidal…

Q: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

A: Here we see the shape of curve in planes.

Q: Consider the function f = x->sinx. Compute the value of f(x) at x = 1.2, then find the derivative of…

A:

Q: The following differential equation- O True O False dz xt-y 1+1 is an ordinary differential…

A:

Q: Simplex Method - Minimization problem   A company wishes to minimize cost of production…

A: The given LPP is  Minimize Z=22x1+33x2+11x32x1+2x2≥20x1+x3≥15x1+x2+x3≥20x1,x2,x3≥0 subtract the…

Q: The following differential equation t²()*+ x = 0 of order 4. O True O False

A:

Q: Approximate the following integrals using Gaussian quadrature with n = 3 and compare your answers to…

A: As per the policy, we are allowed to solve one question at a time. So, I am answering the first…

Q: Consider the accompanying matrix as the augmented matrix of a linear system. State in words the next…

A: What should be the second elementary row operation performed? Select the correct choice below and,…

Q: (b) Use the adjoint method to obtain the inverse matrix of P and hence. solve the system of linear…

A: Introduction: The transposition of the cofactor matrix for a given matrix is known as the adjoint of…

Q: 1. a. Show that this model has an unbounded solution by Big M Method.     b. What can be changed to…

A: 1. (a) Given,               Max Z=3x1+6x2subject to       3x1+4x2≥12    -2x1+x2≤4and      x1, x2≥0

Q: (у) ну- (-см ) - уве Сай

A: Given differential equation is xy - dydx = y3e-x2

Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. 4 A = + 4 5 3

A:

Q: is de -Idc 0 K f (at) = { 1 de (b) Fourier coefficient, a If ripple-free load current in…

A: As per the question we are given the periodic function f(ωt) and we have to find the Fourier series…

Q: Evaluate: S ○ (2-√2) T 8 ○ (2-√2) T 4 O (√2-2) T 4 O (√2-2) T 8 -y² sin √²+y² dady x² + y²

A:

Q: t if n is a of by com

A: Given as, n is an integer 3n+2 is even

Q: 4. (-3x+2y) dy + (-3y + 2x) dx = 0; y(3)=8. Determine y(5).

A: The solution is given in the next step.

Q: Q#7) compare the maximum error, average error, and RMS error for the f(x) = x³ - 3x to the data…

A: Introduction: In analysing the curve fitting for the given data points, the maximum error, the…

Q: a) Find the directional derivative of the function at the given points in the direction of vector v.…

A: Let us consider the given function f(x,y) =. The directional derivative of the function at point P…

Q: Question 2 Let f(x, y) = 8√x - y²e-4xy + ] Find fx and fy. Evaluate fxxy(4, -1). a) [ b)

A:

Q: Problem 1: Solve the following assignment problem shown in Table using Hungarian method. The matrix…

A: As per the question we are given a 5×5 matrix which we have to solve (find the optimal solution)…

Q: 2t e - (₁ _2 ) x + (²₂²²) 4 -2e¹ x' =

A:

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the following…

A:

Q: The solution of the following non exact differential equation (cos x) dx + (1 + ² sin x)dy = 0 is: O…

A:

Q: After representing the population in a given week as a column vector v=[n;p;h], where n,p, and h…

A: Given information:- Among those who are negative, 95% remain so, 4% become positive, and 1% need to…

Q: لعدا - Pa عام ا و لعائله

A: We need to check/find the following: (i) Is g one-to-one? (b) Find a possible formula for the graph…

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A:

Q: Find the solution of the given initial value problem. y (4) 10y""+ 25y" = 0; y(1) = 10 + e³, y′(1) =…

A:

Q: Prove that if the polynomial f(x) = x²n + a₁x²n-² + ... + an-1x² + an is divisible by g1(x) = x - 1,…

A: To Prove- Prove that if the polynomial fx = x2n + a1x2n-2 + ⋯⋯ + an-1x2 + an is divisible by g1x = x…

Q: Evaluate: So SY SY ㅇㅎ 01 21-13 dyde O-3 이용 2 12+y2

A: To Evaluate: ∫03/2∫x/32x-x2dydxx2+y2.

Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated  problems.These…

Q: Evaluate: S 2y+3 (y-1)(³-1) dy ° − In\y − 1| − § (y − 1)³ + ¼ln|y² + y +1| - O √3 ○ – In|₁¹|- (y −…

A: We will use partial fraction decomposition to solve the given integral .

Q: Evaluate sin-¹(3x) dr.

A:

Q: ) ) Given a set of data points (t.. yi) as below ty 1 10 2 5.49 3 0.89 -0.14 5 -1.07 6 0.84 The…

A: Given that: Set of data points=ti,yi, t y 1 10 2 5.49 3 0.89 4 -0.14 5 -1.07 6 0.84…

Q: Exercise: 6 1. (dy/dx)-2y tan x=y² tan²x. Ans. (-1/y) sec² x=c+ (1/2)x tan³x

A: