Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

Q: Evaluate ∫y0ksin(kx−π)dx where y and k are independent of x, and y is given by the solution to the…

A: Given:

Q: 1 2. Evaluate =dx using the trigonometric substitution x= 2 tan0. 2 Vx + 4

A: As per honor code, we will answer the first question for you. Please submit the other as a separate…

Q: Solve the following equation algebraically for the exact value of x. sec-1 = tan-'(x) %3D

A: Hence we get solution  x=212

Q: b. y - y'cosx = y² (1 - senx)cosx

A: Introduction: The Bernoulli's equation is an extension of linear first order differential equation…

Q: ANSWER iv dx ANSWER S sin(ax) cos(ax) dx

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Q: • Tt X 2. sin? cos cOS dx 2 2

A: To solve this I have used the Beta Gamma Integrals. Some of the Results which I have used is given…

Q: Find the general solution of the equation. xsin ydx+ xcos ydy +2 sin ydx =0

A: The solution are next step

Q: Eliminate the arbitrary constants from the following equations. y = e−3x(a cos 5x − b sin 5x) + cx

A: If we have to eliminate arbitrary constant then we have to double differentiate above function with…

Q: Solve the following equation. sin u cos u = 0, 0 … u 6 2p

A: Here, sin (u) cos (u) = 0 By using zero product property, sin (u) = 0  or  cos (u) = 0,

Q: S"(e*sin²x – e**cosx) dx B)

A: The formula of integration using by parts:       ∫fg' =fg - ∫f'g

Q: Which of the following substitutions will convert the differentia equation to a Bernoulli equation?…

A:

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: OBTAIN THE GENERAL SOLUTION 1. X cos? ydx = + tan ydy

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Q: (z) = #, Which of these is a valid solution to the equation tan ( x V3

A: To find the solution of: tanx=33

Q: 1. Find 2 for y defined implicitly by the equation tan(x?y*) = 3x + y?

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Q: The value C in y = sin (Bx +C) is called the _________.

A: The given equation is y=sinBx+C

Q: {2ху — tan y)dx + (x? — xsec?у)dy %3D 0 - -

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Q: Derive y = e*+1 sin x³,

A: To find the derivative of the given function we use product rule of differentiation,  chain rule of…

Q: solve the bernoulli equation dy/dx+y = y^2(sinx+cosx). and show that the answer is y(cosx+Ce^x)=1

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Q: 2) Find of the following equation then simplify whenever possible. and dx dx2 x = 1+ Sin t y = Cos?…

A: The given parametric equation,   x=1+sin t, y=cos2t

Q: Find the general solution to the following equation y" (0) + 3y'(8) + 2y(0) = sin 0 – cos 0

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Q: tan x- 2x°y = c 3

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Q: y(1) = yo + A cos(@t + p)

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Q: The following equation is correct: 2 sin(x) cos(x) dx CoS(2.x + C

A: We will use ∫ & mθ = -cosθ

Q: Sec A - cos A is identically equal to

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Q: a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

A: To find dy/dx.

Q: Find the amplitule of y=-3 sin 4x, A Find the period of fea)=4cos 3 (x-)

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Q: 3 – sin x = cos 2x

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Q: Which of the following trigonometric equations has a phase shift of 1/3 to the right? Oy = cos(x +…

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Q: dy 2y =x'cos 3x dx

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Q: Solve the following Riccati equation dy _2 cos? x – sin² x + y² 2 cos x y1(x) = sin x dx

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Q: I. Solve the following equations on the interval [0 < 0 < 2T]. 1. 1+ sin 0 = 2 cos? 0 2. sec? 0 +…

A: 1+sinθ=2cos2θ1+sinθ=2(1-sin2θ)1+sinθ=2-2sin2θ2sin2θ+sinθ-1=0(2sinθ-1)(sinθ+1)=0sinθ=12,-1θ=π6,5π6,3π…

Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

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Q: How many parameters do we have in the equation y = a cos bx + c sin bx + 4

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Q: sketch r= la 2 Sin'co+)

A: r=1-2sin2(θ+π3)

Q: -y'-Tany = x" (n # 0) 1 Cos?y

A: We change it into first order linear equation and then solve.

Q: Evaluate dy/dx for each of the following equations. a) y=tan-1(x/2) b) y=sec2(x) c) sinx-cosy-2=0…

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Q: In Va? + b² dx In x arc tan- Jo (x + a)² + b² where a and b are real.

A: We will prove the given identity by solving the integral using appropriate substitution.

Q: 7. The period of the equation of motion given by x(t) = 6 sin (4t) is ( a) πs (b) 2 s (c)는s (d) 0.5…

A: Time period

Q: Find the given 5x? cos 2x dx. Using this: "uv – f v du"

A: NOTE: Refresh your page if you can't see any equations. . use integration by parts take

Q: Solve for the general solution of the following equations dy d. sinx+ ( cosx) y=sin( x²)

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Q: I cos 2x dx D.

A: Solve intregal

Q: If y=tan(arcsec/x), then dy/dx is A none of the given choices x-1 2(х-1) sec (arcsec/x) 2x…

A: We have to solve as per usual question

Q: T/2 (cos(7x) + T) dx? 0.

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Q: Differentiate the following equation.  y=cos^-1(2x)

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Q: Eliminate the parameter t and graph the resulting equation.   x = 3 + 2 sin t, y = 1 + 2 cos t

A: Given  x=3+2sint, y=1+2cost⇒sint=x-32.........(1)cost=y-12.............(2)

Q: (cos x cos y – cot x)dx – sin x sin y dy = 0

A: Given Equation  (cosxcosy - cotx)dx-sinxsinydy=0 Given equation is in the standard form Mdx+Ndy =0…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.