Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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

A: To evaluate the given definite integrals.

Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: Solve the tollowing D.E Y+49= cos X sinx %3D

A: The given equation is a second order linear, non-homogeneous differential equation with constant…

Q: Determine the solution to this DE: Cosx dy +(y- cos"x)dn = 0 cos? x Idx = 0

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

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

A: Use seperation of Variables.

Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: Find a particular solution to y" + 36y = 24 sin(6t). %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: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

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Q: cos²x sinx dy + (y cos³x - 1)dx = 0

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Q: 4. J (cos x – sin x)²dx

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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*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

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

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Q: T/2 cos t dt 1 + sin²t

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: The general solution of the D.E. dy/dx + y cotx = 1 is a. y -cotx + c sin x b. y = -tanx + C CSC X…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

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

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Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: Evaluate f sin (3t) cos(3t)dt COS Select one: sin (3t) +C a. b. sin(3t) +C sin (3t) + C d. sin (3t)…

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Q: 6) F Sin12y Cos’ y dy

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

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Q: Find Lt+1)²-e' sin² t + cos(t+1 ++ π)}.

A: Given :

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: T=V3 + cos 0 is given by:

A: Trrr

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: 1 dx J 3 sin x+4 cos x+3

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 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: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

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Q: Find the particular solutions satisfying the given conditions: dy a) y = 2 when x = 0. dx = 1 + cos…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

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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Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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Q: D. ( [ 3° cos"(5t) dt sin(z)

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