(10) Find the general solution of y" − x²y' + xy = x - if a solution of homogeneous part is y₁(x)

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A: To determine the Wronskian of the functions  in the interval , we'll first compute the Wronskian…

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A: The Integral Test is a method used to determine whether a series converges or diverges. It states…

Q: Find the General solution of y" - 4y' + 4y = 9te

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Q: Given is the following inhomogeneous linear system of equations. λα + 2z = 1 Ay - 2 = 4 y + λε = 3…

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Q: 3. Prove that the cube roots of 1 are given by -1+i√√3 =3 2 || 2 -1-i√√3 w³ = 1. 2

A: DETAILED SOLUTION IS PROVIDED BELOWExplanation:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3. Solve the homogeneous differential equation " + 3y" - 4y = 0

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A: We will find the solution of the given differential equations.

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Q: Find the solution of y" - y" + y' - y = 0, f(0) = 1, ƒ'(0) = 3, ƒ"(0) = 1.

A: We have to find the solution of the differential equation

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Q: 2) a) A table of values of a function g is given. Use Simpson's Rule to estimate f₁1.6 g(x)dx. x…

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Q: 3. Prove that 6">5"+9 for any integer n ≥2.

A: To prove that 6n>5n+9 for any integer n≥2, it will use induction.Basis Step:First, will verify…

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A: The proof is given using the properties of eigenvalue and eigenvectors.Explanation:Given:• T…

Q: tions. Find the General solution of y" - 2y' + 5y = 4tet with Real valued func-

A: We have to find the general solution of the differential equation.

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Q: Q2/Solve only three of the following differential equation: 1- y' = xy 2- xy' y+x3 + 3x3 - 2x 3- 2xy…

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A: Gradient vector (7,3)Tangent line is 7x+3y=42Explanation:Step 1: Step 2:Step 3:Graph 1 is the…

Q: . By the method of variation of parameters, solve the following differential equation - y" + (1…

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Q: Find the general solution of this equation: 9y" +6y' + y = = t² t

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Q: Find the matrix A such that 10 -1-3 443-13 Hint: Let A = [26] cd 6 A = -4 0 -3 1

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Q: Let f(x, y) = 4/x+5/y+ 6x + 7y in the region R where x, y > 0. Explain why must have a global…

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Q: 3 b) please

A: f(z) = (z−zi​)31​ + 8 z−(i−3)z−(i−3)​ + 6ez-iExplanation:Here's the justification:a. Pole of order 3…

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Q: Let A is a 4 x 4 matrix such that Ar=0 has non trivial solutions. Is the matrix A invertible?…

A: If the equation Ax = 0 has non-trivial solutions, the matrix A is not invertible.Explanation:Steps…

Q: (4) Solve the following differential equation y″ – 2y' + 10y = g(x), y(0) = 0, y'(0) = 0, y" where…

A: Final Answer: y(x)= 2/3 e^x (sin3x-3cos3x)+1/10 g(x)  CHECK THE IMAGES BELOW FOR COMPLETE SOLUTION.…

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Q: 2) For x 0 solve the Euler equations a) 2" b) x²y" xy + y = x 5/² e³. --

A: The differential equation is :The aim is to solve the differential equation

Q: defined as follows: 1} and consider the inner product on F(X) (f,g) = f(-1)g(-1)+2ƒ(0)g(0)…

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Q: (1) Define the function f : RR by f(x) at a = 1. 2 X x2 x <1 x≥1° Show that f is continuous

A: অতএব, f a=1 এ অবিচ্ছিন্ন।Explanation:

Q: B: Solve the following equation by Finite Differences Method, choose h = 0.25 d²y dx² 2-y=x+y '…

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