What is the equation of the curve that passes through the point (1, 3) and has a slope of 2 x+3 O 9 y = ( − 3x² + ½ x + 0.804) ³ O y = (2x² + 2x - 3.920) * O y = (2²1x² + 2/2 x − 0.804) ³ - ° y = (2x² + 2x - 3.920) 333 at any point (x, y)?

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A: 2.Solution:29+281+2729+.......29+292+293+.......this series is geometric series.Common…

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A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

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A: This given differential equation is 2nd order homogeneous linear differential equation .

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A: The differential equation is given by,  t2 y'' - 4t y' + 6y = 0  Given,    y1 (t) = t2

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A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

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A: Solution is given below:

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A: To find out the general solution of the differential equation.

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A: To solve the following problem

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A: Given :A=420210-2-11B=2312-2-2-121C=31-3026-121

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A: The given integral values,    ∫09f(x)dx=36 and ∫79f(x)dx=12

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A: Here we have to solve the differential equation.

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A: According to our guidelines, we can answer only one question or three subparts of a question.other…

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A: In this question we have to Integrate using the method of trigonometric substitution.

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Q: Solve the given initial-value problem. y(x) = y" + 6y7y = 11e2x, y(0) = 1, y'(0) = 1 2x -7.x 7e +…

A: We can solve the given initial valued problem .

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A: To solve the given integral problem by substitution.

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A: See this solution in below

Q: (B): If A = 2i + 3j-4k; B = 3i-4j+ 5k and C = i + j-k, find: (iv) (3A + 4B). C (1) A.B (U) B.C (iii)…

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Q: 19. For a given function, f(x) = ³ - 15x² + 48x + 2, (a) Find the interval(s) on which f is…

A: Note to student :    Thanks for posting your queries. But there are  multiple parts given. As per…

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A: I have stated the used formulas in the solution

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sinx+cos x sin³ x cos³ x

A: Since multiple questions are asked, I am answering first question

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Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.