5. Which of the following is a TRUE statement? (5/4)! e-2s e-s+5 A) L{t5/4} = $9/4 B) L{u_2(t)} C) L{e&u1(t)} : 58 3! D) L{t°2} E) L{5 cos %3D s4(s – 2)

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Q: 2. By hand, sketch the following against independent variable t: a) x₁(t) = Re(2e(-1+j2m)t) b) x₂(t)…

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Q: dx 2 arctan(4)- arctan (2)-a 4 arctan (5)- none of the choices 3 arctan (2)-

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Q: Find the solution. (D4+2D³ + 10D²)y =0. y = c,+c,x+e¯*(c,cos3x +c,sin3x) C B y = (c,+c,)x+e-(c,cos3x…

A: Given Differential equation is D2+2D3+10D2y = 0

Q: (12) The value of "sin(5x) cos(3x) dx A) 1 B) 2π

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A: Topic :- Derivative Correct option = C

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Q: 6) Use Linear Property to find ( 1- 3 x4)' A) (1- 3 x4) %3D B) – 4x3 C) - 2 D) - 12 x3 7) Use…

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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A: To solve the given differential equation first we construct auxiliary equation and then solving the…

Q: If f(x) = cos (-x) + 3x + 2, xE [0,1], then f"(5) = %3D A) cos + 17. B) cos()+17" (Sm C) 0. D) 2. E)…

A: Solution of question as follows

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Q: 4. Find_r(t), if_r'(t)=4sin(2t)i +8t³j and r(0) = 8i-3j. A) r(t)=-2 cos (2t)i+2t¹ j B) C) r(t)=-2…

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x? cos 2x b) y = cos (sec2 3x) c) y = x²(x³…

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Q: 6) Let f f(x)dx 16, f(x)dx 10, fdx 5 then f(x)dx = A)-1 C) 31 B)-11

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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.