y = C, sin at + C2 cos at, (a not to be eliminated)

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

A:

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: How to compute Cp using below equation, OP, sin 0; Cp, = 2 sin? 0; +2 cos 0 dy dy Where y = 0.5x…

A: To simplify: CPi=2sin2θi+2dθdyisinθi∫0yicosθdy

Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

A:

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: O. p. S sin 2x cos 3x dx 3dx /1 + 9x²

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Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: 1. S sin’y (2 – 3 cos y)°dy

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Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

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Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

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Q: 3. Find y' for y= cos(sin² x) 4. If x=y√/1-y², find y dx

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Q: dy If x=5+ cos20 and y=3- sin20 , what is dx

A: We have to solve the problem

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: H 2= x? tan y/ at (lo1) %3D Ex by

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Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

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Q: S V sin(y) × cos*(y)dx × cos° 3 х COS

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Q: 4. J (cos x – sin x)²dx

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Q: y = (sin x +cos x) sec x = sec² x

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Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: 1(siny) dx dy = %3D

A:

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: 3. S sin x In(cos x) dx

A: According to company rule, we can answer only first question.

Q: At what points the curve x = 2a(cos(t))-a(cos(2t)), y = 2 a(sin(t))-a(sin(2t)) has vertical and…

A: Given: The curve equations are shown below. x=2acost-acos2ty=2asint-asin2t Calculation:…

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. [* sin' y cos' ydy 3

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

A: Topic- Derivative

Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

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: 4. Find the solution of the equation = e * cos y dy? which tends to zero as x → 0o and has the value…

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Q: 6) F Sin12y Cos’ y dy

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Q: トキ 4 Sin Yx cos? dn SinYy

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Q: F(x, y) = 3x – 4y3 + 5x°ys + cos(x) – 3 sin?(y) |

A: Given query is to find the partial derivative onnf the expression.

Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

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Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: satisfied

A: We will solve the problem.

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: ∫sin^6 y cos^4 y dy, limits from 0 to pi/2

A: Consider the definite integral ∫0π/2sin6y cos4y dy to solve this integral, use the below reduction…

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: Solve by Bernoulli's Equation 2. sin y(x + siny)dx + 2x?cos y dy =0

A: We find the solution by Bernoulli’s Equation.

Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: gives – sin(y)ÿ = cos y = x, so implicit -1 - csc y = rentiatio dy dx

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Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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Q: 25. (2y cosx + sint x)dx sin x dy , when x =y = 1 %3D %3D

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