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: A cubic epline Ss defined by (2(G)% 3(x-1)+24-1) -(x-1) 5.(x) = 4 + 4(x – 2) –(+– 2)² +=(x - 2)* S…

A:

Q: 16. If mZJKL = (8x – 6)° and mJML = (25x – 13)°, find m.JML. %3D K M

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: If y = (4r² + 1)* (1 – 2*²then A y' = -4x (4x² + 1)² (1 – æ*) (æ + 6) B None of the given choices O…

A:

Q: (s-1) (s+3)(s²+2s+2) Find L-1

A: To find:-

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

A:

Q: Let 2a4 + y* + 23 = 4 Then dz (1, 1) = 8/3 -8/3 none of the listed here 1

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: 5. (x²-x)? 5.*- 5. - x2 – 2x + In|x|+C x3 2 6. S(6Vx – x-3)2 dx 6. 18x? + x3/2 8 1 + C 5x5

A:

Q: (1) 2x₁ + 3x₂ = 8 x₁ +4x₂ = 9 (Ans. x₁=1, x₂ =2)

A:

Q: 21 (s+ √2) L-¹ {-

A:

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: Find y". 25. y = x/2 - 5x 26. y = x2/3 + 4x 28. y = (x* + x)2/3 30. y = 2x5/4 + x!/2 27. y = (x³ –…

A: The given function is y=x32-5x

Q: x² - 2x x3 3x² - - dx -In 1x³ 3x² 1 + C Option 1 Option 3 - -In 1x³ 3x² 1 + C In 1x³ 3x²1+ C Option…

A: SOLUTION-

Q: 3. 2y"" − 3y" – 3y² + 2y = (e*+ex)²

A:

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

A:

Q: Suppose that you have $11,000 in a rather risky investment recommended by your financial advisor.…

A:

Q: 5. Solve: (1 + + In x + dæ = (1 – In x) dy

A:

Q: Find the series solution for (4x² +8x+5)y" - 8y = 0 about x =

A:

Q: d) ( 2x2+10x (x²+1)2 x²+10x

A:

Q: 11. One of the following could be a series solution for y + 5xy + y = 6 lnx + 4 where y (1) = –1, y…

A: Taylor series of a function f(x) about x=a is given by:…

Q: 4-¹ {√ 5. L- -48 se (3s + 2)(s - 2)

A:

Q: L{5cosh2t-3sinht} 1. 5s 3 a. s²-4 s²-1 3 5s b. s²+4 s²-1 3 5s C. s²-4 s²+1 5s 3 d. s²-4 s²-1 - +

A:

Q: (6) s(4) + 4s(³) + 5s(²) + 4s' + 4s = 0.

A: (.) Given differential equation is,     We find the solution by the method of differential operator.…

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

A:

Q: then m = (q²b²³) 1/10 9-1/261/5 = and n = qmbn 1/10

A:

Q: 3x³-28x² +40x-42 3x² - 4x+5 dx

A:

Q: Problem. Show that S {₁ 【 (s − 2)(s − 3)(s — 6) J L-1 -6)} = 1/2 ²² - e³t + e

A:

Q: Ex:- Min Z= X-3 X2-2 X3 %3D sub to 3X1 - X2 + 2 X3<7 -2 X + 4X2 く12 -4Xi+ 3X2+8X3 slo Find anew…

A:

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

A: Given integral, ∫x3+4x+4x2+4xdx

Q: 11. In(5x + 2) = In 4 + In (x + 3) %3D

A: Apply log properties for solve the value of x

Q: 2x1 + x₂ + x3 X₁-2x₂-3x3 = 1 3x₁ + 2x₂ + 4x3 = 5 (Ans. x₁ = 1, X₂=-3, X3 =2)

A:

Q: 4. Is (1,5) a solution of 3x-2y S-4

A: Let's find.

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: Inverse Laplace F(8) = 4₁+3 (8-1) (5²+1)

A:

Q: Which of the following lines pass through the point (7, 5) and is perpendicular to the line X + 3y =…

A:

Q: 12. (x' + 5x + 4)dx n= 6 0.

A: We have to find the given definite integral.

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.