Find the solution of the initial value problem: [у"+9у-0, у(т) -3, у (п) —-3] а) Оу-сos(3х) — 3 sin(3x) 3x b) O y=-3e* +xe* с) О у--3 сos(3х) — sin(3 x) d) Оу--3 сos(3x) + sin(3x) e) O y=e* - 3xe* f) O None of the above.

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: Place these trig equations into general form: 1.   y = 3/2 cos (πx - π) 2.  y = cos(2x - π) 3.  y…

A: As per our per our guidelines I am solving only first three parts plzz repost other part To place…

Q: What is the particular solution of the function 3e" sin 5x – cos 5x? A cos 5æ + Bsin 5x + C'e" cos…

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Q: Find all solutions to cos(7x)−cos(x)=sin(4x)cos(7x)-cos(x)=sin(4x) on 0≤x<2π30≤x<2π3

A: We know, cos(a)-cos(b)= -2sin(a+b)/2*sin(a-b)/2....(i)

Q: If y = cos x + sin 2x, find the value of y" - y + 3) O 2 cos x + sin x – 2 cos 2x – sin 2x O 2 cos x…

A: Given that: y=cosx+sin2x

Q: Use the method of undetermined coefficients to solve the initial value problem. 33 y ==cos2t 10 33…

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Q: Use the method of undetermined coefficients to solve the initial value problem. y = y = y = y = y =…

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Q: Solve in interval [0°,360°). sin² 10z + cos² 10z = 6 cos z 80.41, 260.41 80.41, 440.41 80.41 ,…

A: It is known that sin2θ+cos2θ=1 for all θ.   Use the above known fact in the given equation and…

Q: "(등 -2) + ain (품 + 22) The simplified form of cos 22x) + sin O V3 cos 22x + sin 22x O v2 cos 22x + 2…

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Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

A: A detailed solution is given below.

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: 8. -dt 1+64t 2 sin-8 B. А. (). -1 2 tan 2 tan- 8 O c. D.

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Q: The standard form of 3dy-xydx = 3y3e4x/3  by Bernoulli's equation is:

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Q: Solve for QIF 4 Cas G+2 sin 2Q+3in 203D0

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Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: 24. Evaluate: S(cos 2x) esin 2x dx A. -e sinzx + C esinzx +C C. esinzx + C esinzx D. + C В.…

A: using substitution method to solve integration

Q: 21. Integrate x cos(2x² + 7)dx. sin (2x²+7) 4(x²+7) B. sin(2x²+7)+c A. +C C. D. 4 4 sin(2x² +7)+c…

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Q: S cos(3z)sin1º(3z) dz C 1 (cos (3z))10 + C 3. (sin(3z))10 + C D 1 (cos (3z))1 + C 33 (sin(3z))'l + C…

A: Topic = Integration

Q: 3) Solve 1−sin2(A)+1 = 2cos(A) over [0,2π)

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Q: The particular solution of the following equation by using the method of undetermined coefficients 2…

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Q: 1)f sin 4xdx cse(2+3lnx) dx 2) fcos 2xdx 7)f sec (4x)dx 3) fx tan(2x2 +1)dx 8)fx csc| 3- dx 3 dx…

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Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

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Q: 2. Explain why (sinx – 2)(cosx + 2) = 0 has no solutions.

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Use the method of undetermined coefficients to solve the initial value problem. O y y = y = y = 33…

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Q: If 1, = |x" sin8x dx , Then 64 I,+n(n-1) I,-2 Select one: O- 8x" cos8x +n x" 7 sin8x O + 8x" cos8x…

A: Given :  In=∫xnsin8xdx                1 Using Integration by parts…

Q: 4. Find all solutions of sin x+ 2sin x cos x-0 if 0sxS2.

A: Note:  As per our company policy we need to answer only one question each time so, please repost the…

Q: The general solution of y" + 16y3 cost is: Select one: a. y= C, cos(4t) + C2 sin(4t) + 1 -tcost 15 O…

A: Using Solution of Linear Differential Equation

Q: capacitor is constructed with two parallel metal plates each with an area of 0.61 m2 and separated…

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Q: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

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Q: Solve the equation in the interval 0<0< 2r. sin (40) - sin (20) = 0 What are the solutions in the…

A: Solve the given equation

Q: the solution in the interval from 0 ≤ θ < 2π sin2xcosx + cos2xsinx = -1/2

A: Given, sin2xcosx + cos2xsinx = -1/2 So, we know sin(A+B) = sinAcosB +cosAsinB  So, let's assume A=…

Q: 9) Show that the equation x+ sin x=1 has at least one solution in the interval0,

A: Given equation is x+sin(x)=1 which can be written as f(x)=x+sin(x)-1 We need to prove that f(x) has…

Q: if we let u-4x- 1 for the 2 tan(4x-1)-3 cos (4r-1) dx, what will be the resulting integrand? cos…

A: The given integral is  (2tan(4x-1)-3cos2(4x-1))/cos(4x-1).

Q: 11 csc²(3x) cot(3x) dx =, (Use Substitution Method) 11 11 +C 6 sin (3z) 6 11 11 +C 6 sin (3z) 6 11…

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Q: (9) Verify that yp = sin 2x is a solution of y" – y = -5 sin 2x and use it to find the general…

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Q: The simplified form of cos G- 13x) + sin + 13x V2 cos 13z + 2 sin 13æ O v3 cos 13z + sin 13x O cos…

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Q: 7. Algebraically solve for 0 < x < 2n a) 5-3 cos(2x) = 5+ sin(2x) а) b) 3 sin(x) = 1+ cos(2x)

A: We know, cos(2x)= 1-2sin^2(x).

Q: Solve x4) +6x³y/3) + 25x²y +19xy` +81y=0 where x>0 O c, cos(3/nx) + c,sin(3/nx) + C3cos(3/nx)inx+…

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Q: Find the particular solution using the initial condition. y' sin(2y) - cos x = 0, y() = 0 O y = cos…

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Q: By using the method of undetermined coefficients, obtain the general solution for у" - 2y' - Зу %3 2…

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Q: 1 Solve sin(x) + 2 O on [0, 27] || -

A: We will find the value of x in given interval.

Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: The general solution of y"+ 16y3cost is: Select one: а. y = C, cos(4t) + C, sin(4t) + tcost 15 b. y…

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Q: Solve the initial value problem y′′ + 9y = cos(3x)+sin(3x) for y(0)= 2, y′(0)= 1.

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Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b