Determine the general solution on the given D.E. by using Separable Method: sin a sin y de + cos a cos y dy

Q: Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy…

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Q: Find the value of integral | (x + y + z)ds, where C is parmeterized by 7(t) (12 sin(3t), 10 cos(3t),…

A: Let’s suppose that the three-dimensional curve C is given by the parameterization, x=x(t), y=y(t),…

Q: Solve the integral equation S" F(x) cos px dx = ' - P.01 4. .Hence prove that o sin?t -dt = %D

A: Given the integral equation is ∫0∞Fxcospxdx=1-p,0≤p≤10p>1

Q: Solve the given differential euation: + rtan 0 = 6cos0 r = (60 + C') cot0 )r= (60+C) sin® r = (60 +…

A: Explanation of the answer is as follows

Q: 1. Given that x = 3 cos nt, y = 3 sin at and z = 4nt with 0<t<1. Evaluate (x + z) ds.

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Q: 4. 1+(sin (20))2 6 cos (20)d0 4. 1+ (sin (20))2 6 cos (20)d0 a f(u) du where g(x) =u, to evaluate…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 2 cos x – sin xy; x = y = 8t t' Enter…

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Q: sin xdx 3 S cos° x

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: (a) Find out solution of the following 3rd order ODE: y" – 4y' – 4t + sint – tet = 0 - -

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Q: Obtain the DE given the general solution . y = c, + C,x + C,x³ + (c, +c,x)e~Và« + (cq cos 2x + c,…

A: We will generate auxiliary equation from the roots of it

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: Find x(t) and y(t) by substitution/elimination. dx 9y + 20 cos(t) dt dy dt 10 cos(t) x – -

A: System of linear differential equation:

Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: Evaluate the following integral. T/2 1 1/4 . sin TX cos 2y sin 2z dy dx dz 0 0 0 T/2 1 1/4 sin TX…

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Q: Consider y(5) + y" = 1+ cos( – t). Then a suit- able form of the particular solution can be written…

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Q: A. Solve the following 1" order, non-homogeneous linear ODE: dy cos? x sin x +y (cos x) = 1 dx

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Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: There exists a solution, F(x,y)=Dc, to (2- 2aye) da – (2ye + 3 sin y) dy = 0 such that - OF 2ye 3…

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Q: u" (x) = – sin(x), 0 < x < T, u(0) = u(7) = 0.

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x y = 7t t' Enter…

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation Lz of a function fz at the point z=z0 Lz=fz0+f'z0z-z0

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; x = y = 7t t' Enter…

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: and its solution EE{ Jm(VAmr) |amncos mô cos( /amict) m=Oh=1 и(r, 0, t) %3 + bmncos m0 sin(VAmict) +…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x : y = 4t t' Enter…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; x = y = 6t t' Enter…

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Q: 1. Evaluate ∫(6w+12) sin^2 (w/9) dw by using integration by parts technique.

A: givenI=∫(6w+12)sin2(w9)dwwe know trigonometric…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: - (7- dy sin2x ) dx = 0 y y

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Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. (A y(t) =…

A: Given differential equation is y'' + a2y = 0; y(0) = 1, y'(0) = 0

Q: Find a positive value of k for which y=sin⁡(kt) satisfies d2y/dt2+16y=0.   k=

A: Double derivative

Q: What is the general solution to the DE, !! dt 2? - 2x + 2? What is the general solution to th O In…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x – cosx = 1, y(0) = 0 COSX In (1 + cos x) = 1 + e² O (1…

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Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

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Q: Solve the integral equation* 1-a, 0 sas 1 0 ,a>1 . f(0) cos ae de = %3D Hence evaluate sin t dt.

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: Solve the following DE, using Separable method. y'In ly| +x*y =0.

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: Solve this DE by Separable method  1. (x2+6y2)dx-4xydy=0 ; y(1)=1

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Q: Find the solution by separating variables. Utt = 4uxx (u (0, t) 3D и(2,t) 3D 0 u(x,0) = sin³(,) for…

A: Given a hyperbolic equation, utt=4uxx with initial and boundary conditions as follows,…

Q: USE HOMOGENEOUS LINEAR HIGHER ORDER DE 4. y(4) + 50y(²) + 625y = 0 ANSWER: 4. y = (C₁ + C₂x) cos 5x…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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Q: Solve the following DE: [2х+ усos(ху)] dx + x cos(xy) dy%3Dо O sin(xy) - х2у? -с O cos(xy) – x?y? =c…

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