Find z(t) for X(s) = -2 s(a+1)(s+9) Select one: O a. z(t) %3D%3D30(1) + 끓etu(t)-공cos3t. u(t) + 끓sin3t. u(t) O b. x(t) = -8(t) +e tu(t) +cos3t. u(t) – sin3t. u(t) 10 O c a(t) = -0(t) +e tu(t) – cos3t. u(t) + sin3t. u(t) %3D O d. (t) = -8(t) +e u(t) – cos3t. u(t) + sin3t. u(t) O e. r(t) = -5(t) +e tu(t) -. e 4.cos3t. u(t) + .e 2. sin3t. u(t) %3D 16 Of 교(t) 3 -금이(1) + etu(t) + .e 2.cos3t. u(t)-.e 2* . sin3t. u(t) O 9.z(t)%3D-이(1) + e tu(t) +끓cos3t. u(t)-옮sin3t. u(t) 26 O h.교(t) =D -금이(t) + e'u(t)-.e..cos3t. u(t) + .et.sin3t. u(t) Oiz(t) =D -8히(6) + 끓etu(t)-.e2과. cos3t. u(t) + 쮸.e 2. sin3t. u(t)

Q: sin (t) -dt 3 (4+ cos (t))?

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Q: f(csc x cot x + 3x2)dx csc x – x3 + c csc x + x3 + c - csc x + x3 +c .3 x° + c O cotx + x3+c

A:

Q: X+1 dx (x- 1)(x² + x + 1)

A: The given integral is: I=∫x+1(x-1)(x2+x+1)dx

Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: (D² - 4D + 5)y = e*; y a. y= e²*(C,cos2x + C,sin2x) – –e 10 b. y e2*(C,cosx + C,sinx) +e 10 C. y =…

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Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: 1. Let A = 2 + €12, B = (1 + e₁). Consider, 1. AB 0 thus BA = 0 also. 2. ABBA 0. 3. ABBA # 0. Choose…

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Q: Solve the equation: (D² - 1) y = 0 Oy=c₁e* + c₂xe* + c3 cos x + c4 sinx Oy=c₁e¹* + c₂e + c3 cos x +…

A: A detailed solution is given below.

Q: cos2x – sin2x cos2x For +C: What is F(x)? dx= 3 cosx - sinx

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Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: xsin ax 2 2 (x²-x²) 1/2 Show that [²= - dx - TV J₁ (ay) 2

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Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

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Q: (D² – 2D - 3)y = 2sin x a. , =cosx -sinx =-cosx -sinx c. = -cosx +sinx COSX 1 b. yp С. Ур 21 COSX d.…

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Q: (3) csc (3x) dx = A) In csc (3x) + cot (3x)| + C C)-In |csc (3x) - cot (3x)| + C B) - In |csc (3x) +…

A: We will solve this question by substituting the value of 3x.

Q: (2x + 1)(x – 1) dr 9. 3x + 6 d.x 2.x3 10. | (20 – 1)(x² + 5)dx 17. - (3x – 2)2 - 18. 4x

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Q: [9x cos(3x + 8) dx = Select one: a. 3x sin(3x+8)-cos(3x+8) O b. 3x sin(3x+8)+cos(3x+8) C. d. + C + C…

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Q: Зx2 — х + 3 dx I (x – 1)(x² + 4)

A: .

Q: dx 1-S 1-sinx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: [ arctan (1-x)]² 4x2- 8x+8

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: (D³ - 3D2 + 9D + 13)y = 0

A:

Q: 2x+1 10x+5 + dx 2. Show that (* +1)(2-x) x +1 2-x (4x² + 4)(2–x)' . Hence, find

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Q: Evaluate L{2t e2t sin (3t) – e3(1-1) + 3et sin (4t – 5)}

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Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

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Q: b) if J(zf64)} - 39ga) ) ce = Sin () %3D and S(3f (x)+9 6)) dx = tan () 2. 2. +596)) dx

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Q: TT Q3(a)- P.T B(m, n) = 2 [? sin2m-10cos2n-10 d0. b. Also verify part (a) with counter example.

A: We have to prove that  βm,n=2∫0π2sin2m-1θ cos2n-1θdθ And also verify this with counter example

Q: Q1/ A: Find: 1 L-1 55+4 2S-18 5²49 24-30 √S + 54 2- L (t² cos at)

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Q: d (c) (cos(2²) + In(3 – 2æ)) dx

A:

Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

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Q: (x+1) dx Vx²+2x+1

A: We have to calculate the integral of the given expression   the given expression is ∫(x+1)x2+2x+13…

Q: Evaluate L{t cosh 4t. 1 1 + (s – 1)’' (s+1)* А. В. (s-1)* (s+1)* 1 1 С. (s –4)° (s+4)' 3. D. (s-4)*…

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Q: f(sin (6x))³ dx

A: According to our guidelines, we can answer only one question or the first three subparts of a…

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.