d² dx dx 3. di² +2 +5x = sin 21, given that when t = 0, x = 3 and dt dt 53 [ 55 Ans. e 17 cos 2t + - sin 2t -(4cos 2t -sin 21) 17 34

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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Q: Q2- (75 %): Classify and Solve; d?y dy cos? t + cosht + sinh t + sin? t +3 sin t - 3t + 9 %3D dt2 dt

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Q: dx Suppose x and y are functions of a third variable t. If sin2(x) + cos2(y)= and dr dy 1. what is…

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Q: 1 s |49 – s2| ds = -14 49т? sin( x dx 14 dt = t2 – 14t + 50 ||

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Q: 15. Solve d²y +3 y + 2y = 3 sin x, given that when x 0, y =-0-9 Wor, OFer dx? dx dy =-0-7. dx and…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler method with h=0.1, y(1.3) = y(A)…

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Q: 4 T 40 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: Solve the definite integral

Q: 57. The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin 21 m/sec for all…

A: We will use the definite integral to find the value of ' s '.

Q: 1. F{(t³ – 3e*)²} 2. Ąe-2"cos3t + 5e-2'sin3t} 3. A(t² – 4t + 2)e³} 4. {3t*e¬6*cost} 5. A4t²sint –…

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Q: a. 9(t) = | (2(t – 1))' sin(4r) dr L{p(t)}(s) = ct b. y(t) = -7(t-T) cos(77) dT L{p(t)}(s) = %3D c.…

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Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

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Q: Q1: Find 1) e (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 4) l (3t5) 5) e (est + cos 3t)

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Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: 2. Find L{f(t)} if f (t) = = cos 4t + t-1/2 + e5t – sin 3t – 5t – 1.

A: We will use the formulas Lcos at = ss2+a2Leat = 1s-aL(sinat) = as2+a2L(tn) = n!sn+1 Hence we have…

Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: Q2- (75 %): Classify and Solve; d²y +9 dy dt2 cos? t + cosh t + sinh t + sin? t + 3 sin t- 3t dt

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Q: Show | S a² sin®(e*) dæ| < 16n*. 8 Show | S, x2 sin°(eª) dx| < 3

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: -Зп 3 cos? x sin x dx 3 cos?x sin x dx 4. a. b. 2т f(1 + t*)³ dt F(1 + t*)³ dt 5. a. b. •Vī t(1² +…

A: 4. We have to evaluate the values of   (a). (b)

Q: (In a + 12x y cos a + x*y cos x)dx + (8xy cos x + 2x"y sin x)dy = 0, 4 2 y(T) = 1/27 b. y da - a(a?…

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Q: A yoyo bounces up and down in the vertical direction with its acceleration after tt seconds given by…

A: d^2y/dt^2 = a(t)

Q: 2 4x (a) S rdr, (b) § sin 0 d0, Cos2/3 g do, (c) St(2t – 5)" dt.

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Q: If x = 3 sin t and y =2 cos* t , then find dy at t = dx 4 O a. -0.67 O b. 0.76 O C. 0.56 O d. -0.86

A: Given x=3sin4t   ,y=2cos4t

Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

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Q: 41. * + 4x + 5x = 8 sin t ; when t = 0, x = 0, x = 0. Note that i = is a common notation when the…

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: x" +4x'+ 3x = 30 cos(3t), x(0) = 1, x'(0) = 2 Solve the above IVP and then find x(0.25). Put x(0.25)…

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Q: Given dy find y 6 cos 6x dx O sin 6x + c O 6 sin 6x +c O-6 sin 6x 0-36 sin 6x

A: Given problem is :

Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: 18. dx/dt = e'(1 + sin t)/(1 + cos t). Answer: [x – e' (tan(t/2)) = C]

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Q: Q1: Find 1) l (3 + e6t)2 2) l {e¬3t (t + 1)²} 3) е sin 3x dx dt 0. 0. 4) l (3t5) 5) l (e5t + cos 3t)

A: We can solve these problems by Laplace transforms.

Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

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Q: Solve the Bernoulli's equation given below: dy 2 dx -y cot2x = y' csc2x O A. [(y )^(- 2)] sin 2x = -…

A: Use Bernoulli theorem to solve

Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

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Q: T/2 | cos(x)/1+sin(x)dx = 6. A. 2/2-1 (2V2 -1) 2V2 +1) В. С. D. 3 (1-7*) Е.

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Q: dx dt (b) 3x – 6x = sin 2t given that x = 1 when t = 0 (c) i- 7* + 12x = 2 given that at t = 0, x 1…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: evaluate the triple iterated integral.

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Q: (a) L{t + sin 4t – e2t cosh rt} (b) L{e' + cos 4t U(t – 1/2)} - (c) L-!{ s + 1 (s +2)(s² + 2s + 5)…

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Q: 4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

A: Okay I am explaining the marked step.

Q: 4. Solve for in the equations below: dx a) -1 dy y? dx b) cos x – sin y 2 = 2- 3 ) xe+ e = 3"

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Q: (5) (2x – y) = 2y – x | dx (6) (02 + 1) cosr dr + 20 sinr de = 0 %3D

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Q: 1.) dx = t (1 + t2) sec?x dt ans: 2x + sin2x = (1+ t?)² + c

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: به)ک ن ان -)f Ssin*(x)cos°(x)dx du )کی + 207 - )J No appropriate Match au)قی - 207 - ه-)J du )کی +…

A: Find the integral match of the integral sin5xcos5x.

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: III. EVALUATE THE FF. ITERA •rU/2 ptan y sec y 1. . x' cos ydxdy Jo . cosy sin2x dy dx xp, •3n /2 pn…

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