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)

Q: Part 1: 1 1. S *(In x)3 dx 2. Se3x cos x dx 3. S(1 + x²)e-*dx 4. So x²e*dx

A:

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

A:

Q: √4x+4-√√5x+1 x#3 Q18) if f(x)= x-3 k x=3 A) 15) 1 C)O by Q19) Use local linear approximation in ind…

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Q: 921) Which of the following is an odd function A) cos xsin x 11 sec.x C). DUNK DOOV

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Q: 4. Evaluate -2π 1 (a) √² indy. (b) fo 3+sin 1 2+cos y dp. (c) f 1 (2+cos y)2 dp.

A: a. The given integral is: I=∫02π13+sinφdφ               I=2∫0π13+sinφdφ               1 Use…

Q: L' (s²+4)(s²+9) 3 f cos(2a) sin[3(t – æ)]dx O b) cos(2t) sin(3t) c) None of these 1 * Só cos (2a)…

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Q: Ql:- Calculate the expression sec3.42x-5 +In4 cos30)2-4x 2 where x = 2, y = 5.…

A: Topic-Function

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: (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: 2s+3 F(s) = ;L-1{F(s)} =? %3D (s+2)²+9 Select the correctresponse: O f(t) = e-2t (2 cos 3t –sin 3t)…

A: Inverse Laplace Transform: Let    be the Laplace transform of that is then is called the Inverse…

Q: Q17) The slope of the tangent line of the curve x² + y²=5 at the point (1,-2)- A) √√4x-4-√√5x-1 x-3…

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Q: The S- 3 dx is 5 sin 6x

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Q: which one one of the following statements. As incorrect 55 @B = [²16 SAT -5 ]-XBT)T=B --26 Sint -9 b…

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Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

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Q: 8t Lle sin 5t cos 5t] = O a. S-8 2 (s – 8) + 100 O b. (s - 8)+ 100 OC. 1 2 (s-8) +100 d. O d. No…

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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: 4. (i) Given that z = ete, show that z" +z- = 2 cos ne. Use this result to express cos$e in terms of…

A: 4i)

Q: a) f(4x)dx x)cx

A: ∫02f4xdx Now, solve the above integral, ∫02f4xdx=∫01f4xdx+∫12f4xdx=f4·1-f4·0+f4·2-f4·1=f8-f0=1-0=1…

Q: 3) Suppose I want to use a "u" substitution to find sec² (9x + 4)dx. What should I choose for u? O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Q1 // Choose the correct answer for the following :- 1- L(e"sinh*t) = a);G-→ »G *9G- 2-L(12cos2t) =…

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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

Q: Which of the following is equal to P (3r² + In(5x) – sin(r))? dr 5 (a) 6x +- + cos(r) (c) r + +…

A: Here given  ddx3x2 + ln(5x) - sinx Therefore , now calculating derivative of given function we get…

Q: Mp=-x Cs 2X

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

Q: sinrdr In(cosr – 3) | cosr -3 A cosr – 3 B In (cosr – 3) In (cosr – 3) cosr – 3 D sinr E) None

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.