An Integration factor of this differential equation is .7 3x? + 1 + x3 dy 1 y : 1+ x2 dx

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: E-10: Let f(x) be a non-constant polynomial satisfying the relation f(x).f (y)= f(x)+f(y)+f(xy)-2,…

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: dy = ky dx x = eky y = e-kx Option 2 O Option 4 O y = ekx x = e-ky Optio n 2

A: The given equation is dy/dx=ky.

Q: NOTE: Enter the exact answer as an improper fraction if necessary. A =

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Q: A: By using Linear equation solve the first order differential еquation y' + sec(x)y = cos(x)

A: The given differential equation is;  y'+sec(x)y=cos(x).

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: 10 (5, 10 -x, x>5 x55 Use geometry to evaluate f(x) dx for f(x) = O 12.5 O 25 37.5 Cannot be found

A: Given that fx=5,x≤510−x,x>5 To evaluate ∫010fxdx

Q: Let Sx² + 3 f(x) = l(x - 2)2 if x 2 1° if x < 1 (a) Find the following limits. (If an answer does…

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Q: Set up the definite integral required to find the area of the region between the graph of y = – 23x…

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Q: Give 5 sample problems for Variable Separable (Differential Equation). Provide step by step solution…

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Q: (a) Find the direction angles for the vector ỉ =AB ỉ +CD j +EF k. "Example if A=5 and B=7 so AB=57."…

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Q: dy = ky dx

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y = x²…

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Q: Determine which inverse trigonometric function g has the derivative g' (x) : = -- (Use symbolic…

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Q: uni vectors that stâtêd coi satisly th st cônditi NOTE: Enter the exact answers in terms of i,j and…

A: Given: u=-2i+7j

Q: Consider the equation y"+ay'+by=f(x) where a and b are real constants. If the general solution of…

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Q: Which of the following theorems establishes a relationship between differentiation and integration O…

A: We have to find out relation

Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

Q: Consider the expression: ey = 4x + y* , In which y is an implicit function of x , after derivation…

A: Given problem :- ey =4x+y4 , find y'

Q: Find the exact values of the remaining trigonometric functions of theta satisfying the given…

A: Follow the procedure given below.

Q: 2 2-y Mote: Complete lirst for X, them or Y.

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Q: Compute the derivative y dy dx y = 7x3 – x-4 (Express numbers in exact form. Use symbolic notation…

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Q: Sketch the graph of an example of a function f that satisfies all of the given conditions. f(x) = 4,…

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Q: Find all the values of x between 0 and ë where the tangent line to the graph of y = sin (x) cos (x)…

A: We will use the concept of differentiation to solve this.

Q: Q2/: Full the following blanks by the suitable solution (Undetermined Coefficients method) If y" +…

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Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: Determine which inverse trigonometric function g has the derivative g'(x) (Use symbolic notation and…

A: Given g'(x)=1x2+1 Integrating on both sides, we have ∫g'(x) dx=∫1x2+1 dx

Q: by the suitable solution Full the following blanks (Undetermined Coefficients method) If y" +y = 2x…

A: We have to answer following Questions.

Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: P(x) Let P(x) and Q (x) be polynomials with the degree of Q (x) greater than the degree of P(x) and…

A: Here we have given that P(x) &amp; Q (x) be polynomial such that degree of Q(x) is greater than P(x)…

Q: Evaluate: 2 esindx, for n=8 using (a) Trapezoidal method, (b) Simpsons Method

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: In this we use Lagrange multiplier to find out max/min value for given constraints, so I'm providing…

Q: taylor LnX

A: Taylor series:  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+..... Where centered at x=a.   Given; fx=lnx…

Q: Find the area of the region enclosed by y = 0.75 and a 6 - y". -4 -3 -2 -1 4 5 -2- Use horizontal…

A: To find the area of the region enclosed by y=0.75x and x=6-y2.

Q: Assume that f(x) is a differentiable and invertible function so that f(3) = 4 and f'(3) = .…

A: fx is differentiable and invertible function so that f(3)=4 and f'(3)=12

Q: 269. A bomber plane, flying horizontally 3.2 km above the ground is sighting on at a target on the…

A: We have to find the speed of plane.

Q: Determine the derivative of y. y = ev12x+8 %D

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Q: An object is moving with velocity (in ft/sec) v(t) = t – 16. Find the displacement and total…

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Q: Find the exact arc length of the curve over the stated interval. 1 -2, from y = 1 to y = 2 1 49…

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Q: Consider the function f: R → R define by f(x) = a?x3 + x² with a a real constant , a + 0, We can…

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Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: Find the average value of the function f(x,y)=y2√x +5 over the rectangular region R=[2,4]×[3,4].

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Q: Evaluate the double integral. /| 4x²sin y²dA; Ris the region that is bounded by y = x², y = -x², and…

A: Given problem:-

Q: Let D be the region enclosed by y = 5x, y = x and x = 1. The volume of the solid formed by •…

A: Here we have to find the volume .

Q: 11. ſ sin? x cos² x dx

A: Given ∫sin2x cos2x dxTo find integration:

Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: Find the solution of the following BVP given that y(0)=2 and y(1)=0. d’y_12dy. dx +36y = 0 dx

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Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

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Q: Let f(x) = 10x° + rx? + e2x. Compute f(")(x). (Use symbolic notation and fractions where needed.)…

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