5s+2 L %3D s2+9) 1 5cost+ sint o 1 5cos9t+–sin9t ,o .b O 5cos3t+sin3t . 5cos3t +3sin2t d o

Q: The general solution of (D2-2D+1)y=2sin x A y= ce*+c>xe* + sinx B y=ce*+c2xe* + sinx+cos x…

A:

Q: Find the GCD OF 4xy°z', 8x²y"z³ and 24x'y°z" ? 10

A:

Q: Example 7: Find the solution of y + 2ý + 4y =x cos 3x The chr. Eq. is r? + 2r + 4 = 0 -bt vb2 - 4ac…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Evaluate cos x + 2 cos x +1 dx sin' x sin x 主x+c sin 主tC 3 sin x cos x COS X + x +c cos xsin X 3 COs…

A:

Q: の x?. xy- yーx find %3D of 3 f Fex)こ X²+5x+2 Find f cl Q Let texl= goe) Find fezt ifgeziz=3_ find…

A: Differentiating the functions

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: 8. If sinx = , x is in quadrant II, then the value of cos2x is %3D 17 b) -161 30 161 353 a) 289 c)…

A: Given : sin x = 817 x is in quadrant II.     To find the value of cos 2x.

Q: z cos(2x)) - cos(2x))+

A: here using sin2x = 2sinxcosx                 cos2x = 2cos^(2) x -1

Q: Solve csc y dx + sec²x dy = 0 elect one: a 4cosy + 2x - sin2x = c O b. 4cosy + 2x + sin2x = c c.…

A:

Q: ſcos^4 (2t) dt * O 3/2 t + 1/2 sin4t + 1/16 sin8t + C O 1/4 (3/2 t + 1/2 sin4t + 1/16 sin8t )+ C O…

A:

Q: 3,5'+ 2

A: The given function is 3s+2s2-3s+2 make the partial fractions…

Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: S 3. sin°ydy 1+ cosy

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Q: 37 17 Squeceze theorem to 8how an= 3" Conuerqcnt, Use aveeze

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Q: ∫0π/2[√(cos5t) sin5tdt] Hint: intergration by substitution

A: Rewrite the equation Apply substitution u=√(cos5t)

Q: 6) 1-cosx %3D 1+cosx (cotx - cscx)2

A:

Q: Solve: y/" – 4y" + 53y = 0 O y = C1 + C2e cos2x + C3e-7* sin2x 7x O y = C1 + C2e cos2x + C3 e7"…

A:

Q: Evaluate: e* cos (7e*) cos (4e*) dx - sin (3e*) + –sin (11e*)+C A 22 B - sin (3e*) – –sin (11e*) +C…

A: Evaluation of the Integral

Q: obtan al the real solutons af 4sinhte 4onh 42 -17 sinh3x + 4 sinhzz =0

A: Note that x=0 is a solution of 4sinh4x-17sinh3x+4sinh2x=0.

Q: t[ ( j ) ( f 3 sin Ꮎ cos2/3 Ꮎ dᎾ

A:

Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: sinx sinx +x The integral cosx - e +e -dr may be written as mensinx + pr+ gerx + C, where m, n, p,…

A:

Q: Yp = A1 cos V2t + A2 sin V 2t Which of the following is Yp'? sin v2t A1 V2 Cos /2t A2 V2 O V2A1 sin…

A: Please see the explanation below

Q: dv Integrate 9 + v2

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Q: S -1 sin y³ +1 2 dydx

A:

Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: Find 7s + 15 -7 s2 + 2 15 cos (v2t) + 7 sin(v2t) V2 7 cos(V3t) + 15 sin(3t) V2 7 cos (v2t) – sin(vZ…

A:

Q: Ir x²y" + xy' + (x? - +>v =0 x >0 || | 1 - 2 sinx ,V1=X the following equations satisfied by v and y…

A:

Q: 4/ Prove that: " cos bx dx = (bsinbx +a cos bx]+c

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Q: 9 Jlguull 2(s-1) (s-1)²+9 2et sin3t a O 3e -t cos2t b O e-t cos3tc O .C 2et cos3t d O 3.

A:

Q: 1) Ans. in 2 frvr* +9dx Ans. 98/3 2)

A: Consider the provided expression, ∫2233dxx-x13 Solve the provided integral. Apply the u substitution…

Q: 3) fyArc tan 2ydy

A: The arc tan function is the inverse of tan function. So, the integral becomes, ∫y Arc…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.