Find the general solution of the differential equation. y(4) – 6y(3) + 9y'" = 0 ... y(x) =

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A: Given: f(x)=4x+11 f(x)=2x2-5x-3

Q: each of the problems, solve the given differential equation. 1. y` = x2/y

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Let's find.

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A: y''-36y=0auxillary equation is given bym2-36=0(m+6)(m-6)=0m=-6,6m1=6 , m2=-6

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A: As per bartleby guidelines we only give first question answers.

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A: The function f(x)=12-3sin(x)

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A: Here, the given series is: ∑n=12∞n+5n! Let, an=n+5n!; n≥12

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Q: each of the problems, solve the given differential equation. 2. y` = x2/y(1+x3)

A: Given query is to find the solution of the differential equation.

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A: To find whether the given series converges or diverges using ratio test.

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Q: .2 dx I (w² – 25)5/2

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Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly and…

A: =&gt; i have provided this answer with dull description in step-2.

Q: 32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

A: Given problem:-

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A: We can solve this as follows:

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Q: Example Evaluate +f -P) dpdgdr (p2 + q² – r²) dp dq dr + pq² – pr2 dq dr 3 1 + q? ² – r? } dqdr 3 -…

A: Let's find.

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Q: a. f(x) = 4x + 11 find:f'(-2) %3D b. f(x) = 2x2 - 5x – 3 find: f'(2) %3D

A: derivative

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Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: Evaluate the definite integral. e12. i+ k 12 e12 i-elj+; k 12 e12 -1 12 e12. k 12

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Q: If f(x) = x'+ 3x + 4x + 5 and g(x) = 5; find g(f(x)) %3D %3D O 5x? + 15x² + 20x + 25 O 5x² + 15x +…

A: Topic = Functions As per guidelines , At  a time only one question can be answered. please repost…

Q: x² +64 Using trigonometric substitution, given - dx, the simplified form of the integral is: sec ede…

A: ∫x2+64x2 dxput x=8tanθdifferentiate on both siddx=8sec2θ dθ

Q: Question 1 1 In solving the antiderivative of f(x) = sin(x) + 3cos(x)+3 by miscellaneous…

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