Proceed as in this example to find the solution of the given initial-value problem. Evaluate the integral that defines y (x). y" - 6y' + 9y = e³x, y(0) = 0, y'(0) = 0 - - y₂(x) = C₂cos(x) + C sin(x) + (C5 - 1) cos(x) + Casin(x) = cos(x)log (sin x) — x sin(x) X

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A: Solve the integration

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A: Here we have to use the concept of derivatives

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A: Use: Pascal's method

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A: Taylor expansion of f at x=a : f(x) ≈ ∑n=0∞ fn(a)n!(x-a)n = f(a)+f'(a)(x-a)+f''(a)2!x-a2+...

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A: The given system of equations,1-13-240-30602095-25x1x2x3x4=-14466124

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A: Follow the procedure given below.

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A: The given differential equation,      d2ydx2+9y=2e3x+18x+18

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A: Solution is here

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A: As asked we can answer question no 1 and 4 as below.

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A: See the details solution in below

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A: We have to find derivative of given trigonometric term.

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Q: Q5-Show if the following series are converging or diverge π 1) Σ=1 η 10 Σ=1 (33) 1 της 2) 3) Σ=1

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Q: [x√x + 1dx

A: Here we have to integrate I=∫xx+1dx

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A: Here is the solution

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A: Explanation of the answer is as follows

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A: This question is related to cosine formula of traingle , we will solve it using given information

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