3. Simplify x(t) = 3 cos(27200t + + sin(27200t + to the form x(t) = a cos(27200t + 0) where a and 0 are parameters you need to determine.

Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

A:

Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

A:

Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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Q: -을 x e [T, 3 J Sinx =

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

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

A:

Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: Compute and * for the equation sin(x)e +2z²y = cos(z). 4xz COS ду

A: sinxe4xz + 2z2y = cosz∂z∂x = ?∂z∂y = ?   While calculating ∂z∂x  variable y will be considered as…

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: Q4/ Find only five of the following: 1-[t cos at 2-f(6 sin 2t – 5 cos 2t 6. 3+2S 3-[( 3 t5 – 2 t3+ 4…

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

A:

Q: After many years in business,the financial analyst of a shoe company projected that the monthly…

A: To determine the month when profit is zero.

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: Find the solution of the equation zz + Əx² ay² ich tends to zero as x→∞ and has the value cos y when…

A: Given : ∂2z∂x2+∂2z∂y2=e-x cosy To Find : solution of the Equation

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: 2. Find (in terms of t): x = 2 + 3 sin t y = -1+4 cos t

A: Given data is : x=2+3 sinty=-1+4 cost To find the value of d2ydx2

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

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

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

Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

A: The given integral is: ∫X x dy - y dx, where Xt=cos 3t, sin 3t, 0≤t≤π The components of the…

Q: 1. If x = e²" and y = sin(3t), find in terms of t.

A: According to Bartleby q&amp;a I can attempt only one question

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

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

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Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: x = Cịcos (At) + C2 sin (At)

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Q: What is if z = x'y+ sin(xy²)?

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Q: y" – 4y' + 4y Cos 4x -

A: The given differential equation is y''-4y'+4y=cos4x ...................................... (1)

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

A:

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: T=V3 + cos 0 is given by:

A: Trrr

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

A:

Q: Solve the equation for x in terms of y if x is restricted to the given interval.y = 6 - 3 cos x;…

A: The given equation is: y=6-3cosx, and x is restricted to the interval i.e., 0,π.

Q: f(t) = e¯3t cos ( at + cos ( 2at + 3 2

A:

Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: integrate cos^2(t)*sin^2(t) from 0 to 1

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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: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: v² operates on sin(-3x) + cos(3y)

A:

Q: (b) Determine cos(x²) 2x dx by using substitution method.

A: