| sec (3.r)dr reduction formula (or any other method) =)dx = 1 sec"-2 (ax) tan(aæ) + (n – 1)a n- 2 %3D xp(= sec"-2 n- 1

Q: Find y' for y = ecos x + tan-1(5x) + (5x² + 1) ?

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Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

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Q: e sin r – x lim 4 cos a – 4 O 0.2500 O - 0.2500 0.5000 O 0.5000

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Q: d²y Find С. dx? 1. y= sin 2x +cos² x sin x 2. у- - y= 1-cosx

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Q: 38. A. -arcsin x x Vx2 – a² 39. 1 В. -arccos x a2 + x2 40. 1 С. | -arccot x Va? – x2 - D. -arccs x…

A: Match the following

Q: e) y = In(cos 4 x) f) y = sin² x y = In(cos(e3*)) g)

A: We can solve using first order differentiation (using chain rule)

Q: 1+tan-1x D. y = + sec-1xcsc¯1x + xsin-1x +V1 - x2 2-3tan-1x

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Q: Q3 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: The given function is, y3secx2+y2=cos2x

Q: (5an 20 elan 20 sec²2 Bd ß 1. e?x +2e* dx e* +1 2.

A:

Q: SS cos(x)esin(x)-2y dxdy

A: To evaluate the double integral, first find the integral with respect to x by substitution method.…

Q: y tan x dx + In* ydy=0

A:

Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

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

A: for y , y'=?

Q: 2х —1 The value of| dx is 1+x-x, tan А. 1 В. О С. 1 D. 4

A:

Q: The dy/dx for y=-4x+7 cos x d/dx (-4x+7 cos x )=

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Q: Final Answer for a1,a2,and az a, =S° - -1dx +- " 1dx = ? 2n-T 2n (1)()(x) 1 | 1 cos- (1)(1)(x) a1 -1…

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Q: (T/2 cos® x dx Determine the reduction formula for cos" x dx and then find

A: Given, ∫cosnx dx∫0π2cos6x The reduction for the above integral will be,   ∫cosnx dx=cosn-1x sin x…

Q: (d) a sin 0 d0 + (x³ – 2x2 cos 0) dx = 0 - %3D (e) x dy - [y + xy°(1+ ln x)] dx = 0 %3D

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Q: 4 Find dy/dx for: y = sec?x- tan²x b- y = sec -x) C- y = sin(tan(3x))

A: It is asked to differentiate the following functions with respect to x: a) y=sec2x-tan2x b)…

Q: Solve D.E using Exact from first order (x' +y' )dx+(2xy + cos y)dy

A: A differential equations M dx + N dy = 0 is exact if  My = Nx

Q: se the bisection method to solve the equation x + cos x = 0. Show an appropriate graph. a. b.…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 3ex sec ydy 0 is given by The solution of the DE %3D 1-ex tany O a. None of these O b. -3log(1- e2x)…

A: Given differential equation is  3ex1-exdx+sec2ytanydy=0. We have to  find the general solution of…

Q: A. Find the function f that satisfies the equation / f(1) dt : 2 cos x + 3x – 5. d B. Evaluate: dx 3…

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Q: Find the solution of the equation cos y which tends to zero as r 00 and has the valRe cOS N Then r-0

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Q: Q3 Find dy/dx on the graph y3 sec /x2 + y2 = cos2x at point (1, 2).

A: We have to find the derivative  of given expression at point (1, 2)

Q: Can you help me step by step?

A: The derivative of a function is computed as follows.

Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

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Q: Solve the ODE using Galerkin method for two equal length elements d²U + 2 = 0, 0< x< 3 dx2 if u(0) =…

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Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: b) y" + y' = sin 2x

A: here we need to find the particular solution of given differential equation. the solution is…

Q: Find d²y/dx² implicitly in terms of x and y. 4xy 5 cos(x) = -9 d²y dx² || X

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Q: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

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Q: (d) ſ tan² 3t dt 5 cos? x – 3 tan x dx - (e) S cOs X

A: The integration of the integrals is d) tan2(3t)  e) (5cos2x-3tanx) /cosx

Q: 4- Find dy/dx for: a- y = sec?x- tan?x b- y = sec - x) c- y = sin(tan(3x))

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Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: x²-a? 6.) y'of y = arccos² х-а + arccsc + arcsin- x²-a² a 7.) y"ofy = (x – a)V2ax – x² + a²arcsin…

A: Given  Y=arccosx2-a2x+arccscx-aa+ arcsinax2-a2

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

A:

Q: f Cos 6 x dx 2 Cos ²3x

A: Solving the problem by finding the value of the problem.

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

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

Q: 5 dx Find dx, x> V25x2 -9 1 + C Vi+9x? * 3x /1+9x2 V25x2 -9 + C 5x 3 - InV1+9x2 +3x| +c sin 13x+c 3.…

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Q: dy 2. Find the general solution to the ODE dx 3x %3D x + 1

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Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

Q: Solve the DE X V1-y2 dx – (9+x4) dy=0 A tan-(x2/3) – 2 sin-'(y) =C (B In (9+x4) – 4x2 sin-1 y=C © In…

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Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: به)ک ن ان -)f Ssin*(x)cos°(x)dx du )کی + 207 - )J No appropriate Match au)قی - 207 - ه-)J du )کی +…

A: Find the integral match of the integral sin5xcos5x.

Q: What is general solution of the given ODE. * dy cos? (x – y+ 1) dx .2 COS

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Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.