@ Sahe the wibrating hring problem. uco,E) = u(#,t)=0, u(x,o) = $in (2x) + sin (3x). Uelx,0) = sin(9x) - Ysin(10x), 0£xtT

Q: y = tan(x sin x) O (x + sin x) sec² (x sin x) O (x cos x + sin x) sec² (x sin x) O (x + sin x) sec(x…

A:

Q: sin 3t dt J cos 3t – 1

A: Given: I=∫sin3tcos3t-1dt   ....(1)   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where…

Q: | sin 5x sin xdx

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Q: |x° (x³ + 2)³ dx 2)3 dx

A:

Q: 3) Find y" if y= 9 sin x.

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Q: Prove that sin(x + y) sin(x − y) = sin²x − sin²y. -

A: Formula's

Q: cos (arctan S (B) - arcsin (3)) - 5 5

A:

Q: liu cos? (x) 1- sin (x)

A: Formula used: Sin2x + cos2x = 1 a2 - b2 = (a - b)(a + b)

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

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Q: Give an example of a value of z such that the equation sin(x ) = z is unsolvable.

A: We have to give an example of a value of z such that the equation sinx=z is unsolvable.

Q: The function y = 2x – cos x have two variables (x and y), these variables called

A: Here, the given equation is y=2x-cosx , which is a function of two variables(x and y). The name of…

Q: fsin²7x dx Select one: O a. O b. O c. O d. O e. 7x - sin²7x cos 7x 14 7x sin7x cos 7x 7 7x + sin7x…

A: Formula used

Q: 1. Show that the initial value problem dy +y³, y(0) = 1, dt has a unique solution y(t) on 0 ≤t≤, and…

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Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

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Q: 2 L-1 (s+2)²+3 бе 6e-2t sin3ta O 2e-2t sin/3t0 .b V3et sin 3tco 2/3e-21 sin/3t.a0

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Q: -1 (3) cscx = sin X

A: We have to use proper substitutions and properties of analytic function.

Q: 1 7. sin0 tan0 + cos0 = %3D cos0

A:

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

A:

Q: (g) sin 3

A: To find the value of

Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

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Q: Sin co dx

A: We have to solve the given integral.

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: sin? cos' dx 2.

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Q: Evaluate dx 9. x2 |1 4x2

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Q: L G -S 2 (5² +a²)2 11 t sihat 2a

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Q: cos(Inɔx),>o

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Q: az then x ax az If z = tan tan-1 +y ду

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Q: [17 sin³ x costx dx 5.

A: Given: I=∫17sin3xcos4x dx. To evaluate: Value of integral I.

Q: sin(3t)dt

A:

Q: 30 csc (3x) cot(3x) dx (Use Substitution Method) 30 30 + C 6 cos² (3x) 6 30 30 + C 6 sin²(3x) 6 30…

A: Given that  I=∫ 30csc23xcot3xdx We need to substitute the appropriate value so we can solve it…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.