Find the solution the initial value problem x' -4 -2 -4 х, 3 x(0) -2 x = Choose one Descr n as t |Choos Choose one cos t – sin t - sin t – cos t e 3 cos 2t – 2 sin 2t -3 sin 2t – 2 cos 2t -4t - e cos t – sin t – sint – cos t e cos t – sin t - sint – cost -

Q: 3x 3x 16 cos + isin 4. 4. Sa 5x 34 cos + isin 3 3

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Q: Question 6 Find the solution. (4D3+12D2+13D+10)y = 0. /½(c,cosx+c_sinx) + cge -2x y = c ,xe-2* + e A…

A: given differential equation is  9D3+12D2+13D+10y=0            (i) Solution of the Homogeneous…

Q: L(e-3t (2 cos 5t-3 sin 5t)) 20

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 2. Solve 2 sec 0 + tan 0 = 2 cos 0, 0<0<2n .

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Q: SOLVE THE EQUATIONS

A: Given:

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: cos t 1-sin t sect + tant

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Q: If cos(t) = 1. cos(2t) 4 = 2. sin(4t) = || || = where t = [0, 90], determine

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Q: If A = A-1 = 2e2t sin(5t) 2e²t cos(5t) 2e5t cos(5t) -2est sin(5t) , then 4

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Q: T 10+ f¹(2 cos²x-cosx-1)=8, f(-2)=0, x= 0, 2 Solve for X.

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Q: 3. V2 C T. V2 V2 3 10. sin B =[Select ] 11. cos B = [ Select ] 12. tan B = Select] - -13

A: Trigonometric ratios

Q: 3 sin a If f(x) –, then 2+ cos x 3+ 6 cos(x) (2+ cos (z))² f'(x) = f'(5) =

A: For part (b) just put 5 in place of x in the expression of part (a).

Q: tan 2x sec 2x dx Evaluate cos 2x O 1 ,tan 2x e + C 2 2 e tan 2x + C O -2 e sec 2x + C 1 ,tan 2x + C…

A: ∫etan2x sec2xcos2x dx=∫etan2x sec2x sec2x dx     ∵secx=1cosx=∫etan2x sec22x dx Now put,…

Q: If sin(x+y) - - sinx + 뜰 conx, what is the value of y? O 0 이용 6

A: Topic = Trigonometry

Q: sin(20) cos(20z) dæ- O 100 O 0 O -2 O 2

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Q: TT -1 Cos 2 sin 2

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Q: i) Simplify sin(2sin-1x). ii) Show that sin 30 = 3 sin 0 – 4sin30. iii) By using the substitution 0…

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Q: 0 1 (b) sin 3

A: To determine the value of the theta.

Q: XV3X-4 V3x-4 +C tan 3x-4 +C sin' 2 tan 3x-4 +C sin 3x-4+ C None V3x=4 tan +C 2

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Q: the sum of sin h 2x and cos h 2x

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Q: Š 4 sin(3t) 2+ cos(3t) 7 sin(3t) + dt (2+ cos(3t))²

A: Definite integration

Q: Find (21) (22) if = 5 (cos 75° + i sin 75°) 22 = 5 (cos 35° + i sin 35°) Answer: Z1 = (2₁) (2₂) =…

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Q: (4e" + 5x* + 5 cos x)dx 4e" + x + 5 cos x + c O et – x + cos x + c - O et + x5 – 5 sin x + c 4e" +…

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Q: Question 6 of 10 n(x) = csc°(;w) Select the correct response: csc(-a) + cot(x) CSC - 1 sece'(승)…

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Q: Solve the equation 2 cos²x+cos 2x = x = [0, 2π). 0 where

A: We have to for x

Q: 4 sin² x - 1 2 sin x + 1 2 sin x - 1

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Q: Solve sin 20-2 cos e on the interval 0 Sx <2n. 0, 7 3x ズ 2 2 21

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Q: Cos z+1 cos 2 1 + sec x =

A: Use simple trigonometry relation.

Q: 7. −ydx + (x + √xy)dy = 0

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Q: If, Sec t-1/sec t +1 = A-cos t/A+cos t Then A =

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Q: V3 If sin x = - and -90° S x S 0°, evaluate sin 2x 2 1 2 V3 2 1 2 V3 2

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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.