3. Approximate integration formula | f(x)dx = aof (0) + af(1/2) + azf (1) is exact functions f (x) = 1, f (x) = x and f (x) = x² , find the constants ao, a1 and az by solving a linear system of equation using Gaussian %3D Elimination.

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

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Q: Find the solution to if x(0) = 3 and y(0) = 4. x(t) = y(t) = = = y-x+t = help (formulas) help…

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Q: f(x) = 2- a, r>0 f (z) =

A: Let y=2-x2.

Q: (x-2)(dy/dx) – y =(x-2)3 solve homogenous equation by linear equation method

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Q: Find the general solution of y + (1/3)y = e"y Show your solutions on a separate sheet of paper. A…

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Q: x' = (C )x ´sec X + 0, 1

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Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: - If f(r) = e² is a solution of xy" – (r + 1)/ + y = 0. Then, the general so (A) y = c1e² + c2e=z…

A: Answer is in next step     option  E is correct.

Q: Use D-I method

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Q: What physical systems might the Chini equation, y*y' + f(x) = g(x)*y, represent? Can you tell me…

A: The Chini equation, given by  y∗y′+f(x)=g(x)∗y , appears in various physical and engineering…

Q: Integrate: f'(x) = 4x¯½. A. 2√x + C B. 8√x + C C. √x + C D. -√4x + C 2

A: Integrate: f′(x) = 4x-1/2

Q: se Newton-Raphson Method to find the approximate solution of the nonlinear equation f(x) giv en as…

A: To approximate the solution of the below equation using the Newton-Raphson Method. x3−x−1=0

Q: 2- Solve the following equation: Utt = c?uxx +, u(0, t) = u(2, t) = 0 u(x,0) = x? ,u; (x, 0) = e*

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Q: Jp-1(x) – Jp+1(x) = 2J,(x), %3D

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Q: Integrate: 14 9x²+2x-1 (x-1)(2x²+7x-4) dx

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Q: lIf 90 +9f(x) + x²(F(x))* = 0 and f(3) = -2, find f'(3). f'(3) = %3D

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Q: Use D-operator methods to solve (1) (0²+16)y= tsint Cii) (D²+D+5)y =t coszt %3D

A: Given : i) (D2+16)y=tsint ii) (D2+D+5)y=tcos2t.

Q: Let h(x) f(x) where f(x) = In(3x2 + 2x + 2) and g(x) = -2x. What is h' (x)? g(x)' Select the correct…

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Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

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

Q: [v= -y +2x ,x' = 4y + x + t

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Q: Show that u(x, y) = y²e* + 3x² is the solution for u = yuyy + 6x . 2

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Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: If h(x) = f(x) – g°(x), f'(x) = -9(x) and g'(x) = f(x), then h'(x) is: %3D

A: The solution of the problem is given in the next step.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.