Linear Non-Homogenous – Variation of y" + 4y = cos 2x parameters

Q: (cos x cos y cotx) dx - sin x sin y dy = 0. -

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Q: Determine the local extrema of the function f(x)=sinx−cosx on [0,2π].

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Q: siny dy 2. 3 |- cosy

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Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: cOS X 1. S dx V4-sin²x ´sinx` A. Sin-1(n*) + C cosx B. Cos-1(*) + C В. + C sin 3x . Integrate: S;…

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Q: region. y = x + sin x 4 1+ 2.

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Q: sin 3x 22. Integrate: JS dx V25-cos² 3x A. -sin-1 (os*) + C 'cos3x' (cos 3x` C. -sin *) + C 15 B.…

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Q: 1 -dx cos.x-1 2) Integrate

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Q: I. Find dy -and simplify the result whenever possik dx 1. у%3Dsec3 2х - 3sec2x 2. y = sin (x + 4 )…

A: Given; 2) y=sin(x+4) cos(x-4) 3) y= -3 cot5(x/3)/5 + cot3(x/3) -3cot(x/3) - x.

Q: y = 3x arcsin x = 3x aresin r -1 ons of all tangent lines to the uve slope 2. ation of the tangent…

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Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: cos (In z) sin (In x) dx

A: To Evaluate the integral

Q: | sin“ x cos' x dx 4. Integrate:

A: Given: ∫sin14x cos5x dx  To find: Value of the integral.

Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

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Q: x = -sin 2y x = cos y --

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Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: (cos x cos y cotx) dx - sin x sin y dy = 0 -

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Q: siny dle = (1-x cosy) Cas y

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Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

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Q: (x² cosh(sin(x– y)): - »)= (x² cosh(sin(x – ))= v+coshz ôvôz

A: As per the guidelines I could solve only part 8. But as part 9 and 10 are short to answer, We will…

Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: Sketch flx) = 2 cos x-Sin 2x , osx<2o

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Q: Find F′(x).

A: Fx=∫0sinxt dt=t32320sinx=23sinx32-032=23sinx32

Q: Find the relative extrema of the function f(x, y) = x2 + 1 − 2x cos y, where −π < y < π.

A: Given  fx,y=x2+1-2x cos y,   where -π&lt;y&lt;π Partial derivatives with respect to x and y of the…

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: Find Fourier sertes [o, 2] an 2) fex) f Cx) = Sin X ニ

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Q: cos(xt) cos (sin(at)) dt D. tan x dx =

A: The question is taken from the calculus in which we have to find the value of the given integral, We…

Q: f(x) = cos x + 3, [0, 27], midpoint

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Q: sin Vx z = 1+ cos Vx COS

A: We havez=sinx1+cosx

Q: y = Vsin (x)+ /sin(x)+. sin (x)+ sin (x)+ Vsin (x)+

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Q: Solve using determining the integrating factor: cos x dx + (1 + 2/y) sin x dy = 0. %3D

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Q: Suusn. COS X t cost a) f(x) = (b) y = 1-t %3D 1+ sinx

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Q: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Given function is sin 2x-cos 2xsin 2x+cos 2x. Integrate using integration by parts. Chain rule of…

Q: sin x dy (1 + y) cos x + sin x If y=- , prove dx %3D cOS x 1+2y + cos x-sin x 1+ sin x 1+ 1+ cosx 8.…

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Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: (sin x + cos x)dy + (cos x – sinx)dx = 0

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Q: Determine the general solution of y" + y = tanx using variation of parameters

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Q: cos y sin x Let f(x.y) x+0 %3D cos y x=0 Is continuous at (0, 0) ?

A: Continuity

Q: sin³ydy 1+cosy

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Q: sin(sin 'u - cos v) ed on u and y

A: We have to write the given trigonometric expression sinsin-1u-cos-1v as an algebraic expression and…

Q: Partial Differentiation a2z 1. If z = e* sin y + e³ cos x, verify a²z = 0 ду?

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Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.