3. Eliminate the Arbitrary Constants (C, and C2) in the equation. (25 pts) y = C,cos (At) – C2 sin (At)

Q: b. e4t cos x dx

A: Solution of the problem as follows

Q: 2. Eliminate the arbitrary constants of the equation below, where B is a parameter. x = c1eßt + c2…

A: Given, x=c1eβt+c2e-2βtSin 2t-4t3 To eliminate the arbitrary constants of the above equation.

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: 41. e* sin y d A, R = [0, 2] × [0, 4]

A:

Q: 2. Eliminate the arbitrary constants of the equation below, where ß is a parameter. 4 C₁eßt + C₂…

A: Given equation is x= c1 eβt +c2e-2βt sin2t -4t3

Q: 3. Differentiate the following with respect to the variable: a. y =-2 Lnx – cos 5x + 6 sin 2x – 2 x²…

A:

Q: Solve (by separation of variables) the following problem du = 0 ; x E R , t> 0, t > 0, - и(х,0) =…

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Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

A:

Q: 13. Reduce the equation y + 4 = 0 to the normal form x cos 2 + y sin 1 = p, and hence, find the…

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Q: 5. Solve the following IVP: sin(t) y = -4 cos*(t), y(;) = cos(t) y' + 0.

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Q: e n'rdr 17 cos'x Sin 2. 4

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Q: d. y= cos-x

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Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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Q: *10. cos Z = 0.5234 YX _ y 24

A:

Q: a) y = cos(e 2x) (e2x) -1

A: Differentiate wrt x

Q: Eliminate the parameter: x = cos3 t and y = sin3 t.

A: Given: x=cos3t                                               ..1y=sin3t…

Q: In each of the following, eliminate the arbitrary constants. 1. cxy + c'x + 4 = 0 2. y sin x – xy =…

A:

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

A:

Q: 2. Find the antiderivative of COS -2 sin a Simplify dr

A:

Q: 4. y= e (A cos x + B sin x),

A: Formation of differential equations: As a rule, one reqruires  n+1 relations to eliminate n…

Q: /4 (6) Evaluate I cos y dz dr dy = A. B. C. D. A

A:

Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

A:

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

A:

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: Find the solution of the equation a²z a²z + Әх? ' дуг which tends to zero as x→∞ and has the value…

A: Given: The equation is ∂2z∂x2+∂2z∂y2=e-xcosy. Also, the given equation tends to 0 as x→0 and its…

Q: Which of the following is a particular solution Yp to y" + 6y' + 2y = cos t where Aj are constants…

A: given equation :

Q: 4. What is the form of y, given (D² + 9)y = x + tanx? A. Yp = V,sinx + vzcosx B. Y, = v, sin3x +…

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Q: For which values of t is the curve concave upward? x=cos(2t) y=cos(t)

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Q: 11. sin(x) + cos(y) = ey

A:

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: Solve the following equation using separation of variables: cos(x) dy 2y d.r 1+ sin(x)

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

Q: Find the general solution of the equation cos x cos y dy – sin x sin y dx = 0

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Q: Solve the following Bernoulli's equation by using an appropriate substitution. sin y (x + sin y)dx +…

A: We have to solve the give Bernoulli's equation by substitution.

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: cos (y) C = 3x2

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Q: t/2 SL cosx/1+ cos²xdxdy is equal to 0, siny

A: Consider the iterated integral, ∫ab∫f1xf2xfx,ydydx In this iterated integral, the integration is…

Q: 3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Where does the periodic function f(x) = 2ešin (x/2) take on its ex- treme values and what are these…

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Q: If L(ešt + cos(3t)) = As²+Bs+C (s–5)(s²+9) the value of C is

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Q: @2) find to dx 2. y=CoS 2' Sin e

A: To find the dy/dx of the given function

Q: Show that y = e²(cos x + sin x) is a solution to the equation

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Q: 7+2 sin y -dy = D cos ?y

A: on solving this we get the