Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy = 0

Q: Given that cos(x) = (-1x2 for e<xc than a powr saries of cas(x) %3D ie e (2n)!

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Q: The appropriate change of variables for the dx is Vx²+2x+10 O x=10 sinØ O x+1=3 sinØ O x-1=2 tanØ O…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: Separation of variables.

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Q: Answer the following neatly and completely. Find dy/dx. 1.y = sin(x²e3*) 2.y = In (tan x?) .xcos y –…

A: Chain Rule of Differentiation : If we have y=f(u) and u=g(x) then dydx = dydu·dudx

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Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

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Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

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Q: solve for y in terms of t or x, as appropriate.

A: Solve for y in terms of x :     lny2-1-lny+1=lnsinx

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A: Part(c): Given function is, fx=x33x-4 at 4,2 To find the gradient of a function (which is a vector),…

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Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

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Q: (1 + cos 7t) 2 sin 7t dt

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

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A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

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Q: .2 x cos?y dx + tan y dy = 0

A: The given differential equation is  x cos2y dx+tan y dy=0 Solving the the given differential…

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A: The given ordinary differential equation is of the form:

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: Find by definition for the following : dx 1. y = (2x² + 1) 2. y = cosx 3. y = sin?x

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Q: Solve the given higher order DE y" – y" + 3Dy – 5y = e*Sin 2x

A: Auxiliary equation corresponding to given differential equation: m3-m2+3m-5=0 Roots of polynomial…

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A: To Determine: Differentiate the given function:…

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Q: Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy 2. = (-5x + y)² –…

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x² cos 2x b) y = cos*(sec² 3x) c) y = x²(x³…

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Q: 2. Prove the following equation is exact and hence find its general solution. (y?sinx + xy?cosx)dx +…

A: Given: (y2sinx + xy2cosx)dx + (2xysinx)dy = 0 To prove that the above equation is exact. We also…

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Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

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Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: Given the implicitly defined function 6. cos (2*y) – y* - cos(2r) – y? dy and dr dr find at the…

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

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A: Solution of following equation using separation variable 2ydy/dx= cos(x) /(1+sin(x))

Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

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Q: 2 Without using technology, sketch the graphs of the following for 0°<x < 360 a y = sin æ + 1 90 180…

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Q: H.W. 1) Lt² sin wt 2)L t cos wt 3)L t² sin 4t 4) Lt³ cos wt .3

A: Recall the Laplace's Transformation, L{tnf(t)}=(-1)ndndsnL{f(t)} where L is LaplaceTherefore,…

Q: H.W Find y' for y = ecOS X + tan-(5x) (5x2 + 1)?

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Q: Solve the following DE: [2х+ усos(ху)] dx + x cos(xy) dy%3Dо O sin(xy) - х2у? -с O cos(xy) – x?y? =c…

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below