SOLVE THE NHLDECC USING UNDETERMINED COEFFICIENT (D² + 1)y = cos(x) ANSWER: y = C1 cos(x) + C2 sin(x) + '2 x sin(x)

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

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Q: 2 y = A cos 4x + B sin 4x +sin 3x b) 7

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

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Q: Find the solution of the equation = e Cos y which tends to zero as x → 0o and has the value cos y…

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Q: 6. Solve cos.xdx +|1+= sin x dy = 0 y

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Q: Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²)…

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Q: y = c, e2* cos 3x+C, e²* sin 3x

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Q: sin x – e-* = 0, [0,1]

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Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

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Q: G- tanx) ydx + Inlexy cos x| dy = 0

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Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: 8. Find all solutions of the equation in the interval [0, 2n) a) sin(x+ t/2) - cos?x = 0

A: The trigonometric equations are:          sinx+π2-cos2x=02cos2x+7sinx=5 The interval for the…

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

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

Q: 2x cos x? dx 1+ sin² x² 8

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Q: 3e" + 3x + 10 cos x + 2)dx .2

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Q: Find the solution of the equation = e Cos y which tends to zero as x - 0o and has the value cos y…

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Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: 8) Determine the smallest positive roet of the equation - 0.0i t sin (0.573t) -e

A: To determine the smallest root of the given of the function we will use Newton-Rapson method with…

Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

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Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

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Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

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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: 2. xy' -y == y cos 3x

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Q: Find the solution of the equation cos y which tends to zero as x- 0o and has the value cos y when x…

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Q: 1. Consider 3x + sin x – e* = 0, using Secant Method with initial points xo = 0 and x1 = 1,…

A: The given equation is; 3x+sinx-ex=0.

Q: Find the general solution to the DE using the method of Undetermined Coefficients: y" + 9y = 2…

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Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

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

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Q: 2) x³y? = 2x + 2y3 3) y = sin?(x) – cos³(2x) + 2 www. .

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Q: Find the solution of the equation Cos y which tends to zero as x - 0o and has the value cos y when x…

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Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: 11. sin(x) + cos(y) = ey

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Q: у" + 4y' + Зу %3D sin (e*)

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Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Determine the general solution of y' = cosx cos y

A: we have to find the general solution

Q: Find the general solution of the equation cos x cos y dy – sin x sin y dx = 0

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Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: solve the nonhomogenous equation y''' - 6y' = -cos(x)

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Q: 4) e (). – | T|x² – 4| CoS - 2 2x sin sin² ( T|x² 19 dx 2 -3

A: Integrate

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

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Q: E valuate dx 7-3 Sin X +6 Cos X

A: solution.

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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

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