The general solution for Legendre equation (9- 2)y"- 2ay' +n(n + 1)y= 0 is O y(x) = c1y1(x/3) + c2Y2(x/3) none O y(x) = C1y1(3r) + c2Y2(3x) O y(x) = C1y1(3x²) + C2Y2(3r²) O y(r) = ciy1(r/3) + C2y2(x²/3)

Q: 1 (g) √ F+x(a+b)+abdx

A: To evaluate the following integral.

Q: er + e-x3 d) k(x)= 3e* + 4x

A: Given function, k(x)=ex+e-x33ex+4x

Q: f (x) = 2x, g (x) = x + 4 and h (x) = 5 – x³ Evaluate the following: 6) (f + g) (2) 8) (f · h) (–1)…

A: Using rules of function.

Q: Q/IF it was AY ₁2) = -12 Y(2) ℗ Y³ (2) = − 12 ⒸY² (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13…

A: Given

Q: csc -1Vxdx (6) Vx3 -x2 CSC x3-x2

A: From the given problem:   I=∫csc-1xx3-x2dx   So we can also write as:   I=∫--2csc-1x·12x-1xdx.....1…

Q: - 9x - 24 (x + 4)(x + 1) Evaluate ·S -dx + C

A:

Q: x2 + 2y2 + 3z2 = 1

A:

Q: If f (x) = 4x + 3x2 - 5x +20 and g (a) = 9x - 4x2 + 10x- 55, what is (g-f) (x)? 13x – a2 + 5x – 35 A…

A: See the details solution in below

Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

A:

Q: Differentiate y O 1 4x +2 = x(x-1) (2x²(x + 1)) 3(x-1)²(x²+2x+1) 8x² + x 2 2 O3(x-1)² (3x²-1) 8(x² +…

A:

Q: D2 – 5D +6)y=3xex+2x2 , y(0)=0,y,(0)=1

A: Given differential equation is homogeneous ordinary differential equation. To solve this equation…

Q: 3.2 X(x²-1)-y=xy* ;y(2)=-

A:

Q: (x²-x) y¹ = (x²+1) y + 12x (x²-1) ³ y' when x = 2, Y = 9

A: Given differential equation is  x3-x y' = x2+1 y  + 12 x x2-13                      ⇒      x3-x…

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: (х? + 2у — 10у3х) if z у? (у? + 4х + 5у) dz -, find || дх

A: Given:

Q: Example 9.14. Solve yy + (x + 2)y + xy + x² + 2x + 2 = 0.

A: Please find step by step solution below:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: Which of these functions has a y-intercept of (0,9) ○ A) ƒ(x) = 9x² + 4x + 2 B) f(x) = 9(x-3) (x +…

A:

Q: Solve 1og x t1og (x-2)= 10q (ex)

A:

Q: In(7x – 1)= In(3x + 7)

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: /x + 3 + 4 – x > - 3

A: Answer

Q: LAR널)] = Y(S) = [올 +2 Yi(s) = Y,(s) = (S+4)×2 블 +8S+20 N/A ( 52 ) ³²+ + 4 . √2 + 5 - S14 (S+4) e (5²…

A: To show:-

Q: f(x-1) e-2x+x² dx = O 1 -2x+x² e 2 2e-2+2x+C 2e-²x+x² + C e-2x+x² + C + C

A:

Q: (3) J -x² + 4x 2 x³ + 4x² + 4x + 3 dx

A:

Q: Find x, y, z, and w. X = y = Z= W = x 7 (2x y 6 - 5) (2x = ¹) ] - [ (²x - ² 9y Z 9 By + 8) ] 8 (w +…

A:

Q: Suppose that 0.3210 approximates 0.3245. How many significant digits does the approximate have? O 3…

A:

Q: Y1 le-v2(A2(a2-i))-A1(a1-1) dy2 Y1 e-v2(A2(a2-i))-A1(a1-i) (A2(a2-i))-A1(a1-i)|

A:

Q: Can someone explain how this problem is simplified with steps: ((x2 + y2 + z2)1/2) - (x2 / (x2 + y2…

A: In this problem we simplify by taking LCM on left hand expression &amp; hence we get the result on…

Q: Solve 1. (z - 4) s(3z + 2) 2. X+8(x+1) > 3(2-x)+x

A: Given; 1.  (8/6) (z-4)&lt;=(2/18)(3z+2) 2.  x+8(x+1)&gt;3(2-x)+x

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.