Use the method of reduction of order to find a second solution of the differential equation t²y" — 4ty' + 6y = 0, t > 0; y₁(t) = t². - NOTE: y₁ and y2 form a fundamental set of solutions. Y₂(t) =

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

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A: y = x5 y =1  find V = ?   V = π∫(f(x))2dx here we have to find limit of x  here first quadrant given…

Q: Q5: Find for the following functions: dx (4) y = x sinh 2x-cosh 2x (3) y = e* sin² x In√x

A: See this solution in below

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

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Q: 4 2 fcsc^x col²x dx S

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Q: In Problems 17-26, solve the initial value problem. dy y(0) = √3 dx y' = x³ (1-y), 1 dy 2 dx dy…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

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Q: Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

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Q: Which radical function has a domain of (xe Rx≤3) and range of (y e RIy2-4)? Oy--√x+3-4 Oy--√x+3+4…

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Q: Which of the following functions describes the graph of g(x)? -10- + O g(x)= O g(x)= (2) 2²-8 2²-8…

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Q: 4. y = Ae bx are cosax + Bebx sinax, where a and b(lowercase) parameters. (not to be eliminated)

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Q: Use substitution to evaluate the definite integral given below. 1² (Enter an exact answer.) Provide…

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Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

A: I am attaching image so that you understand each and every step.

Q: Consider the position function below. r(t) = (1-1²,3-5t4) for t≥ 0 a. Find the velocity and the…

A: Given;  r(t)=<1-t2,3-5t4).

Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sin6 x+cos6 x sin ³ x cos³ x…

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

Q: Use the disk method to find the volume of the solid of revolution generated by rotating the region…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: To find f'(a) & equation of tangent:

Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

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Q: For the vectors u = (6, 3, 4√5) and v= (3, 0, 5√5), evaluate the following expressions. a. 3u + 2v…

A: See this solution in below

Q: a) Find the area of the triangle determined by the given point P₁(1, 2, 4), P2(1,-1, 3), P(-1,-1,2)

A: As per Bartleby guideline, only the first question has been answered. Please repost mentioning the…

Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: STJ (x (x + sin x) dx Jo

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

Q: Find f'(x) for f(x) = - 8A√x - 5Bx⁹ where A and B are constants. Completely simplify any fractions.…

A: Solution of given question is written in below steps.

Q: 7. 0 , e5) a dx

A: Please see the below picture for detailed solution.

Q: (A): solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: QUESTION 6 Which of the following functions are separable? Of(x,y)=In(xy) f(x, y) = x² + y f(x, y) =…

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Q: Q4: Answer two only: 4 2 (A): If A = 2 l-2 Find AB and AC. 1 -1 01 0; 1 2 B = 2 l-1 3 1 -2 -2 and 2…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: We have to find out equation of tangent

Q: Question 2 Find a differential equation whose general solution is y = c₁est + c₂e-2t. 0 2

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Q: A solid of revolution is formed by revolving about the x- axis the region bounded by the curve y √2x…

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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: Evaluate the following integral. π 2 7y sin y s s dx dy 0 0

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Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Q5: Find for the following fun dx (1) In(x - y) = xy + y² ;

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

Q: (Simplify your answer. Type an exact answer, using radicals as needed.) b. y = (Type an exact…

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Q: 7dx x(lnx + 1) S:

A: To solve the given integral problem by substitution.

Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: 2: Solve the following integrals: - 7x² +14x+15 (x²+3)(x+7) dx ; 1) S

A: Given: ∫7x2+14x+15x2+3x+7dx

Q: Exercise (b) the centroid of the region bounded by the graphs of the equations Step 1 The region is…

A: Please see the answer below.

Q: what about part (b) please.

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Q: 2. What is the radius of the circle defined by x + y² - 6x + 4y - 1 = 0

A: x2 +y2 -6x +4y -1 = 0 here we have to find radius standrad form of circle is (x-a)2 + (y-b)2 = r2…