8. One of the following could be a series solution for y"- xy 0 with y(0) = 3, y (0) = 0 %3D 504 O 1- + 180 12960 O 3 + + + .. 60 4320 O 2 - + * 90 O 2 ++ 90 6480 504 504 252 O 3- 60

Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

A:

Q: X'=x+²* 21 -3 6. t -3 -4 2x e

A:

Q: 1 1.S xvx2-5x+7

A:

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0 %3D

A: 2x+62y2+3dx+4yx2+3x+2dy=0

Q: (4x + 1)2 x2 - 5 Find S' if s = s' =

A:

Q: 5. S(-5x-6 + 10x-11 – 20x-21)(x-5 –x-10 + x-20)dx

A:

Q: 4. Suppose that a single bacterium is in a bottle at 11:00 am. It divides into two bacteria at 11:01…

A: As per the question the bacteria population becomes double every minute and initially means at 0…

Q: The top and bottom margms Op a poster are are 8 cm and Hhe Side mary Ms'are each 6 cm if Hhe ae a of…

A:

Q: 9) (5y + 8y) - (4y + 3y') 10) (2x' + 6x) + (3x - 4x)

A:

Q: x²-3x - 7 √ - (x² + x + 2)(2x − 1) dx

A: Given: I=∫x2-3x-7x2+x+22x-1dx   As we know that; ∫1ax+bdx=1alnax+b+C

Q: For v= 3 compute the following, and write your answers as integers or simplified fractions. w = 3 4'…

A: Given,  v = 13, 23  w = -14,-34  We have to solve for (a), (b) and (c).

Q: 2y4-6x3 +|1x=-37x-16 dx X3 - 3x2+5x-I5 2x

A:

Q: If s = (x² + 1)²/3 (3y² + 8y +4) 4(3z+2) 5, find d²s d²s dy² d²s dz²

A:

Q: 3. Find the correct form of x(s) and stop. State x(s) as a single fraction. x" +7x' + 6x = 2t x(0) =…

A: Explanation of the answer is as follows

Q: d) ( 2x2+10x (x²+1)2 x²+10x

A:

Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: (-2m*)' (2a'6') (32y 13. 14. 8m (2ab*)' 15.

A:

Q: 6. Write the recurrence formula for Zj+1 - the derivative of second degree spline at node tj+1.

A: To give the recursive formula for zi+1- the derivative of second degree spline at the node ti+1

Q: y(k +2) - y(k + 1) + 2y(k) = 2* with y(1) = y(0) = 0 %3D

A:

Q: 4 4 + x2 Find 3 x° + + 4/x ) dx - -

A: Given integral, ∫x3+4x+4x2+4xdx

Q: If C'(x) ME = n=0 (2n)! 2n x²n and Xx ∞ S(x) = Σ n=0 (2n + 1)² series of C(x) + S(x). 2n n=0 (2n) 2…

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Q: 9. (a) Show that if n is an integer, then: -o3* (") = 4". %3D (b) Let n be a positive integer. Show…

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Q: 1. x2+ 2x + 1 0 5x² + = 0 %3D 3. 5x 2+5 = 0 4. 10x* 2x + 1 = 0 5. -x2 + 10 = 0

A:

Q: 5. 2x+3y 39 y-7 =-2(x+ 10) 3. y = -x + 4 y = -2x – 13 + 13 %3D # y = 3x - 13 3. "y=D- y = * + 2 %3D…

A: Given: 5  2x+3y=396  y-7=-2x+10

Q: S' = 4 + ( 20 ) * + ( ਲੰਡਨ ) * ( ) 1 + 2022 * 1 + 2021 2 2 + ... + 1+ + 1+ ² 2021 2020 1+ Find S = ?…

A:

Q: 2 + 5r +4 h(r) = 3r + 5 3r + 10r + 13 O A. h'(r) =- (3r + 5)2

A: The derivative is computed using quotient rule.

Q: X -is If y = x² — xy + 1, then when a = 1, d - 0-1/1/12 01/22 0-1 0-2 O nonexistent

A:

Q: 2(-1)n-1_6" n=1 5n+1

A: To find: ∑n=1∞-1n-16n5n+1

Q: 5. Find y' by Implicit Differentiation for * 2y — Зу? + 4х y' = - 1 y' = 3y – 2 %3D 1-3у O b. a. 1 1…

A: Find out the implicit differentiation of given function.

Q: 4. (3x – y)2 = 6x + 2y + 23 @ (1,-2) 5. x(x² – y²) = 3 @ (-1,2)

A: 4) (3x-y)2=6x+2y+23, @(1,-2) 5)x(x2-y2)=3, @(-1,2).

Q: 4. y" +y = e* +x³ ; y(0) = 2 ; y'(0) = 0 %3|

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Q: y' 3x² + 4x - 4 2y-4 y (1) = 3

A:

Q: 353. y = x-1/2 (x² + 3)2 (3x – 4)ª

A: First, we expand the given expression using properties of logarithm

Q: 7. Find the sum of t + t2 + t3 + . tn + .…. where tn = 8(5)~"

A:

Q: Find LN F *x+2 7. *+10

A: Solution AA (or AAA) or Angle-Angle Similarity Criterion: AA similarity criterion states that if any…

Q: 1+x Show that coth-1x = ; In () 2 x-1

A: We have to prove the given expression.

Q: neN JS E (4i +1) = 2n2 + 3n +1 n(n +1) . neN JI

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.