Determine whether given differential equation is exact. If it is, find the solution. 3y (x² – 1) dx + (x³ + 8y – 3x) dy = 0; y (0) = 1 %3D %3D

Q: Evaluate the following integrals using integration by parts. x5e* dx |x3 In x dx -2x sin 2x dx

A: Hi there!! since you have asked multiple questions, we will solve the first question for you. If you…

Q: Approximate the solution of the equation 2In(sinx) – 5=0 in the 3rd iteration of the Newton Method…

A: The solution at the third iteration is,

Q: State whether the equation is ordinary or partial, linear or nonlinear and determine its order and…

A: To verify that y is a solution of a differential equation, substitute y in the given differential…

Q: 1. Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting…

A: Given, If u = Ln (x) then resulting integral is ∫2u du

Q: a.) Solve the by Gauss elimination. Show all steps of the computation b.) Substitute your results…

A: Rewrite the eqn and apply transformation

Q: Given z= /1+xy and (x,y) changes from (2, 1) to (1.97, 1.04). (a) Use total differential to find the…

A: We have to calculate  z=1+xyby using differential to app. to ∆z and Exact change in z And app. of z…

Q: Find the particular solution of the differential equation yy' – 2e* = 0 that satisfies the initial…

A: use separate method

Q: Use exponential shift to solve the differential equation (D + 2)³y = 0

A: Given,Differential Equation :(D+2)3y = 0Multiply e2x, both sides:e2x (D+2)3y=0 ⇒∫D3(e2xy) =…

Q: Determine the solution set of the following equations using linear equations. 2. (x5 + 3y)dx – xdy =…

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Q: x(3xy – 4y' + 6 ktx + (x² – 6x²y² – 1 )dy = 0.

A: To find the general solution of the given differential equation (DE).   Given:…

Q: dy 6. yz = 1, when x = 0, y = 4 + %3D dx

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Q: Consider H.W.4 a closed rectangular box with a squar base. If base side is measured with evror at…

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Q: 4. 2xydx + (x2 + y²)dy = 0

A: The equation is said to be exact whenever the partial differential of M is equal to the partial…

Q: From the given figure, determine the following characteristics of the resultant: (a) magnitude of R,…

A: Given Data: The length AC is given as 6 ft.   To Determine: (a) The magnitude of R. (b) orientation…

Q: 1. Derive the continuity equation in cylindrical coordinate by using the infinitesimal element (dr,…

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Q: A. Solve the following system of equations by Gauss elimination method. [2 1 1 27 4 0 2 1x2 4. 3 2 2…

A: In Gauss elimination method we  make an augmented matrix [ A : B] and the elements of A below the…

Q: An engineering function is given by a = y?e² cos x At x = 1.3,y = 2.1,and z = 4.9, compute the…

A: The engineering function is given beow,a=y2ezcosxx=1.3y=2.12z=4.9To determineAbsolute errorRelative…

Q: 4. solve the following system by using Jacob's Method with initial value x = y = z = 0. 5x + 2y + z…

A: Note -Since we answer one question at a time so we will answer the first one. Please resubmit…

Q: Find the ratio of E/K if Poisson ratio is 0.02

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Q: Multiply the Following Vectors using cross Product method. W = † x F F = ( 5i + 3j – 8 k) N f = (2i…

A: Given   F= 5i+3j-8k  r=2i-4j-5k

Q: 3. Find the general solution of the DE: y"+ 4y'+ 4y 0.

A: 3) Given differential equation y''+4y'+4y = 0Above differentila equation can be written asD2y+4Dy+4y…

Q: 0.3 0.6 0.9 1.2 1.5 1.8 °f(x)c f(x) 0.5 0.6 0.8 1.3 2 3.2 4.8

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Q: dy Solve the differential equation of - dx A In y = c Inx B) y = c Inx Cy=lnx + c (D) y^2 = In x + c…

A: Given,dydx=ylnxdyy=dxlnxThis is the differential equation of variable-seperable…

Q: Test whether the following differential equations are exact and solve those that are. (y sin x + xy…

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Q: Determine whether given differential equation is exact. If it is, find the solution. (e – y cos…

A: For the given differential equation,

Q: What is the area of the below figure if you know x=35.7? (use Simpson's rule) 33 27 32 28 30 31

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Q: 4. у" + у3 tanx y

A: Given data: y''+y=tanx

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Q: Solve the equation using Jacobi's method until 5 iterations. 5x₁ - x₂ + 2x3 = 12 3x₁ + 8x₂ − 2x3 =…

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Q: 7x+14] -x .What value of x satisfies the matrix equation (2 points Зх-2 5 x+8 5 Solve for x and y in…

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Q: To apply Simpson's 1/3 rule in integration, the number of interval must be? O 1 O 8 O 7 O O

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Q: Solve for one possible solution in the equation, using Secant Method * cos x + sin x – e* + x e-x

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Q: Calculate the general solution of (z + y)dx + (x – y)dy = 0.

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Q: Solve the resultant and magnitude

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Q: 7. dy cos(x + y), when x = 0,y =; 4 dx

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Q: 2. ay + 2xy = x, subject to y(0) = –3 dx

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Q: Q 1: Find the first and second order partial derivatives of f(x,y, z) = x³ + 3x²y + ysinz

A: Given data: fx, y, z=x3+3x2y+ysinz

Q: Q/A) Solve the differential equation ? dy + (cotx)y = sin³x dx

A: answer isy = -14sin2xcosx + 3cosecx8(x-12sin2x) + cexplanation is given in the below step

Q: D. Solve the following by Linear Equations Method. 1. (x* + 2y)dx – xdy 2. y' = csc x – ycot x %3D

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Q: Question 46 cosx dx, which of the following trigonometric identities will be used? In solving for…

A: Given integration of cos3(x) Identity function sin2x+cos2x =1

Q: Determine whether the following differential equations are EXACT or NOT EXACT. If exact, solve for…

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Q: Problem 1. Determine the following unknowns on the beam shown below using Double Integration Method.…

A: Given data: E=200×106 kPaI=0.150×0.150312=42.1875×10-6 m4EI=8437.5 kN.m2

Q: 1. The simplified general solution of (1 – x)y' = y² is

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Q: 1) Expand the given function in a Fourier series f(x) = x(2 – x), 0 < x < 2 differential equations

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Q: Using any Geometric Methods only: (Double Integration, Conjugate Beam, Area Moment) Determine the…

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