(2n Yn+2 + ) yn+1 ) Yn = (2n + 5)2" cos (") %3D 2n+3 2n+

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: Transform the given differential equation or system into an equivalent system of first-order…

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Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

A:

Q: 7x Cos + COS cos 2.

A: According to trignometry formula:cos a +cos b =2cosa+b2 cosa-b2Given,cosx2+ cos7x2a=x2; b=7x2

Q: (b) (cos(x) (2x + 3))'

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Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

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Q: 1. use two iterations to find the solution of the equation In(x) – cosx = 0 With the estimated…

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Q: 2. Solve: sin 3x dr + 2y cos 3x dy = 0

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Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: 2) x- 2y = x°cos4x

A: Given differential equation is -   xdydx-2y=x3 cos 4xDivide throughout by x we get-dydx-2xy=x2 cos…

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: (1+cos(4t) dt 2

A: Let's find integration of given function.

Q: e- + cos (xy) = (4 – 3z) (2 + 2.x), UIM 4. find ду ÚTM az cos (ху) — (4 — 32) (2- 8 UTM UT UTM

A: Partially Differentiate with respect to y

Q: what is the general solution of y''+4y=cos(2x)

A: Given: y''+4y=cos(2x)

Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: 3. 4. 5. π X dx sin() co₂ (:) ª 2x - 1 4x1 dx 8. 9. (x-1) √x dx _2_2x dx 10. S√₁-2² a x dx

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Q: Find the general solution of y" – 3y' + 2y = cos = COS

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Q: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

Q: 3. Solve for x E [0, π) 2 cos²x + 3 sin x = 3

A: Sol:- 2cos2x+3sinx=3, ∀ 0≤ θ<π⇒-3+2cos2x+3sinx=0Use the Pythagorean identity:…

Q: Find the general solution of cosec"x2= cos²y(separate variable) %3!

A: As per our guideline we are supposed to answer only one question.kindly repost other question. The…

Q: -2/√√/3 dx x√√x²-1 • [²/²2 (x + 12/²3). dx sin² π/6 28. • √2 30.

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Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: 2. If y = C₁ cos2x+C₂ sin 2x+2sin x is the general solution of a certain nonhomogeneous LDE, which…

A: The given general solution of non-homogeenous  LDE.  y= c1cos2x +c2sin2x +2sinx   We have to find…

Q: fcos xdx cos xdx 2 Jcos xdx 2. 4)

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Q: (E2-2E+4)y= 2n 6 cos nr+2√3 sin 3 na 3

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Q: &. y = -2 co0(2 -) 7. y = -3 sin 2r + 9. y = 4 sin ( mX 11. y = 3 cos ( TX 2) + 5 12. y = 2 cos (2nx…

A: I have provided solution in step2.

Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

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Q: 8. / (V80 – x² 0.3 cos(1.2x + 1.3) + 5) dx -

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Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: 1. (6x + f²)dx + f(2x – 3f)df = 0 2. (cos2f – 3x²f?)dx = (-cos2f + 2x sin2f + 2x³f)df 3. (fe*f –…

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Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: - 7x +2 g (x) = (x + 1) (x – 5) h(x) = -2 cos x+5 y = 4(x + 1)³ –7 x2 y = 4*+2 f (x) = -3x° + 6x¬² –…

A: To organize the following equations a polynomial or non polynomial.y=15x4-7x+2gx=x+1x-5y=5x2hx=-2…

Q: find a particular solution of y"-9y=-6 cos3x *

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Q: Find all solutions of cos 2x V3 for x if 0 < x < 27. 2

A: on solving this we get the

Q: (cos 6, sin 0) (0,1f G4) 2x (号) (올) 120 3 3n 60 135 45 5x 150 6 30 (1,0) (-1,0) 0,0 180,t 7x 210, 6.…

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Q: 2. 5yl-3y/+2y = t³ cos 4t

A: We need to decide if we can apply method of undetermined coefficient to find a particular solution…

Q: Determine the general solution of: a) -3 sin x = cos 2x b) cos 2x =1-2 cos x ||

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Q: 3 Find all solutions of cos 2x for x if 0 < x < 2n. 2

A: The solution is :

Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: Find the general solution of y +9y-4 cos 2r A. y -A cos 3x +B sin 3x +c cos 2r B. y -A cos2xr + B…

A: Given: y''+9y=4cos2x

Q: 2) S(3x + cos(x))[3x + 2sin(x) -312dx = A)13x +2sin(x)- 3 +C B)13x + 2sin(x)-31 +C C) other

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Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

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Q: 4 Give the general solution to x²y' + xy = -2 cos(2x) y¯2

A: The solution is given as

Q: 5.S Vsin 2x . cos2 x dx

A: Integration is a process of adding up infinitesimally small pieces of an area. There are mainly 2…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.