L[u(t – 3) (r²4' – 9 4')] = 64e- -3s (s-In 4)3 9. (s-In 4)2 2 81e-4s (s-In 3)3 16 (s-In 3)² 64e-3s ( - (s-In 4)3 6. (s-In 4)2 e 4s (s-3)³ 8 (s-3)² In 3 e-4 (름 + 음) 8

Q: d = V(22 – a1)° + (42 – Y1)² %3D - - (8, -3) and (-5, 6)

A:

Q: 32²+4dx Find 3xe 3+4 dæ

A:

Q: Differentiate and simplify: y= (3 – 4x)²* O a.y' = - 2(3 – 4x)²*-4x + (3 – 4x)In(3 – 4x)] Ob.y'= 2(3…

A:

Q: 8. 2.2 dr

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: (2x + 3) = 3y1 4 Select the correct response: O 2+ 12y3 2,2x + 3 3 3 Y 1 (2.x+3)3 o 12y°(2.x + 3)?

A:

Q: Q1 -/m 3 SoNe |3x+1|-4=1

A:

Q: 3x SG / (√²² - 36 - 5√6) dz- +6² √a

A:

Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: - In(1) none of the choices -5 - In(3) - In(4)

A: Integration of Rational Function: A function of the form , whereand are polynomials, is called a…

Q: 4.x²e2" dx 2.21 4. (d)

A:

Q: 4 (0) = 4l6)=3 Soluhon DE: Y= 64,-442

A:

Q: S Vi+ V2+3xdx

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

Q: (2x) (3y+8) (2x+4) R 5. mZQ = mZO =

A:

Q: dx x²(81+x*)3/4

A: Given integral is: I=∫dxx2(81+x4)34 Let us substitute:…

Q: If x = (1/2)a + (2/3)b + (3/4)c c=(12x-6a-

A: The detailed solution is given below Thank you

Q: L4 for x2+1 고 on [-2,2]

A:

Q: 2x3+x-1 4. S x3+x2-4x-4

A: Given: ∫2x3+x-1x3+x2-4x-4dx Suppose I=∫2x3+x-1x3+x2-4x-4dx

Q: YA 7) 3 X+4 3 y>}x-1 2 432 -2 -1 -4 2 3 4 -2 -3 4 -5

A: The given inequality is: y≤-34x+4y>12x-1

Q: 0000 2x/48x5y+ x³ /27xy- x²/75x³y (3v6-2)°

A: x1000y29z=x5002y28yz=x5002y142yz=x500y14yz2)2x48x5y+x327xy-x275x3y=2x2*2*2*2*3*x22xy+x33*3*3*xy-x25*…

Q: 2t/t-2 = 4/t-2 +1

A:

Q: 12 dx x3 - 2x -63X answer In (x -9) 3 I In Xt In (x+7) + C' 12 21 28

A: Solution:GIven∫12 dxx3-2x2-63xFormula:∫1xdx=log x+C

Q: 6. 2e* e3xdx

A: ∫2e3xe3xdx

Q: • 4 13х + 12 -dx x2 + 3x 3

A: ∫3413x+12x2+3x-4dxApplying completion of squares:=∫3413x+12x+322-254dxSubs u =…

Q: хt — х +6 dx х3 + Зх

A: We shall use polynomial long division method to simplify our integrand.

Q: 2 x ×+10メ+3X+36 dx (メー1)(x44

A:

Q: S(in 6x) dx x (In 6x)2 - 2x (In 6x) +c x (In 6x)2 - x (In 6x) + x + C <(In 6x)2 - 2x х (in 6x)2 + 2x…

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Q: 5. c) [(4x³ + -)dx +

A:

Q: 5. S(e2r – e-2r)²dr S(e?r -2т е 2х 6. S dx 4-Зе2х

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Q: (2x + 3)dx 9x²+2x+8 17. S

A: Given that…

Q: (6y² - 3y-8y')-(3y - 2y-5y') Зу

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.