Find d-/dx? at the given point without eliminating the parameter. *=0+cos0 and y= 1+ sin® ; 0 = r/6 A 57 B 2л С) 4 D

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Q: S cos ædx from a = 0 to b = %3D %3D 3.

A: Substitution is done.

Q: Determine the integrating factor of the Bernoulli's equation given pelow: dy -y cot2x = y' csc2x dx…

A: ................(1) substitute take derivative .................put it back in equation 1

Q: IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

A: Solve partial differential equation by Lagrange method. Rewriting partial differential equation…

Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: 2y у'+ — х?у? sin x %3D

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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: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

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Q: S cos“C)dy

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Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: dy iven that x = e" cos 3t, y=e" sin3t, show that tan 3t + dx %3D 4

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Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: 3. Integrate the following dx (i) V9 – x² (ii) ſe-3*cos4x dx (iii) ſ sin³2x dx -

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Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: 3. Arctany dy

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Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: 11. Put the following equation in separated form, do not integrate. do d. + sin 0 = 0 %3D dt

A: Topic - differential Equation

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

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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: T/4 cos vt dt COS T2/36 Vt sin vt

A: Integration by substitutions

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (5t), 8 cos (5t)),…

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Q: 6) F Sin12y Cos’ y dy

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: The integrating factor of the equation sec? y + xtany= x° is: dy de In|sina| O None of these…

A: We have to find I.F

Q: The velocity of a particle moving along the x-axis is given by: v(t) = 1 cos(nt), t>0

A: Use the defination of velocity than solve the differential equation by separation of variables.

Q: cos 2y dy sin y

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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: | sin t cos* t dt 9.

A: We have to evaluate given integral Concept:

Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: 7 Find (b) x siny-ycosx-y 1.

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Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

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

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

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: 5. Find dt ,y = cos(sin(t – 4))

A: Given function is: y=cossint-4 Derivation of the above function with respect to t. dydt=ddtcossint-4

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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