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

Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

A:

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

A:

Q: 10.4y" + 4 = cos-1x

A: 10.The given equation is, 4y''+4=cos-1(x)

Q: Solve the equation on the interval 0s0<2n. V2 cos 0- cos 0 = 0

A: The given equation

Q: sin30 de 10. 1 -cos 0

A:

Q: Find all solutions to 2 sin(0) V3 on the interval 0 <0 < 2n.

A:

Q: Find all solutions of the equation in the interval 0, 2n). sinx+ cos 2x=D1

A: basic formulae required to solve the above question: cos2x=1-2sin2x function positive in…

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: 4. Find the general solution of the equation: cosr– sin 2x =0

A: Use general solution

Q: How do I solve sin(t)−cos(2t)=0

A:

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: . Solve for x: 2 cos x + sin x = 2, 0<x < 27.

A:

Q: plot the graph of y= 1+sin2x for 0&lt; x&lt; 180 and obtain approxiamate solutions from the graph to…

A: Given, function is

Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

A: Given- ∫cos3t dt5+3 sin3t We have to find u which is used in evaluating the given integral and to…

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: е: Solve over the interval [0, 2n) 2cos23x + sin3x = 1

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Q: What substitution should be used to solve the integral x²dx 4-9x2 sinu=3x/2 O sec u =2x/3 O sec u…

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Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

A:

Q: Show work.

A:

Q: Solve sin(6x)cos(11x) – cos(6x)sin(11a) = 0.45 for the smallest positive solution. X =

A:

Q: (2.) (1-(In))^ (3.) yn + sin ()

A:

Q: Q2: Solve the DE y' – 4y = sinx.cos2x by undetermined coefficients method.

A: The given differential equation is                                    y'-4y=sinxcos2x  ......(1) The…

Q: Find all solutions to 2 sin(0) V2 on the interval 0 < 0 < 2n 0 =

A:

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

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

Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

A:

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

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

A: Sol:- 2cos2x+3sinx=3, 0≤ x&lt;πUse the Pythagorean identity:  cos2x+sin2x=1-1-2sin2x+3sinx=0Let:…

Q: find all the solutions in the interval [0,2pi) cos^2 x + 2cosx + 1 = 0

A: let cos x = t t^2 + 2t +1 = 0 (t+1)^2 = 0 t +1 = 0 subtract both side by 1 t = -1

Q: Solve over the interval [0, 2n) 2cos23x + sin3x = 1

A:

Q: Use the method of undetermined coefficients to solve y" – 2y' + y = 5 cos(2x) + 10 sin(2x)

A: Solve the differential equation y"-2y'+y=5cos2x+10sin2x using the undetermined coefficients .

Q: Solve the equation on the interval 0s0<2n. 2 sin20 + V3 sin 0 = 0

A:

Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

A:

Q: dy Solve sin -1 | = x +y dx,

A: Sin-1(dy/ dx) = x+y =&gt; dy/ dx = sin(x+y).

Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: 2:Solve: cos (x+ y) dy = dx %3D

A:

Q: Find the solutions of the equation that are in the interval [0, 2π).

A: We have the given trigonometric equation as cosπx+sinπx=0

Q: ,2 coS“ x cos a – 1 = 0

A:

Q: Solve on the interval [0,2n). (2 cos x + V2) (2 sin x – 1) = 0

A: Some trigonometry angles: 1.)sin90°+θ=cosθ2.)cos(90°+θ)=-sinθ

Q: Find all solutions to 2 sin(0) = v3 on the interval 0 < 0 < 2n. = 0

A: To find solutions of 2sinθ=3 where 0≤θ≤2π

Q: - Tt/2 2 cosx dx 1+ (sin x)2 -T/2

A: Using substitution: So the limits of the integration would be given by: And

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A:

Q: Solve the equation on the interval 0se<2x. sin 0= 6( cos (-e)-1) %3D

A: The solution is given below

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Q: 8. (sin°(5y)dy

A:

Q: cos(2x)cot (2x) 1-sin (2x) = 0

A: Given, The trigonometric equation [cos(2x)cot(2x)]/[1-sin(2x)] = 0 We have to find  all the…

Q: Find the solution of d2y/dx2+4y=sin3x+cos2x

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Q: c) Se- sin(4t) dt

A: