Find the series solution of (4 – x²)y"(x)+ 2y(x) = 0 about xo 1 %3D %3D

Q: S(1 – 2x²)(x + 3)dx

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Q: 42 x²y" – 4xy' + 6y = %3D

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Q: ] Solve (3xª – y)dx + (x – 4x²y³)dy = 0.

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Q: If P(B) = 0.55, P(A | B) = 0.70, P(B')= 0.45, and P(A | B') = 0.90, find P(B | A). P(B|A) = (Round…

A: Given that PB=0.55,PA|B=0.70,PB'=0.45 and PA|B'=0.90.

Q: 5. Solve (y² + 3xy³) dx + (1 - xy)dy = 0.

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Q: Find 4 [3f (x) – g(x)]dx = i if 4 4 |r)dx = 4 and g(x)dx = 20

A: This question is related to definite integration, we will solve it using given information.

Q: n of (3x²–

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: dy Find dx-1 = (5; - x*)() x+1 y =

A: y=5x5-x4x+1x-1

Q: 8) 2x+5y=5 x-4y=9

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Q: 6z dy (78)a

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Q: 1) Evalvate - 5 dx ZV5 arctan x - 5 5 2 /5 arctan X-5 +C 2 x* - 5 arctan 5 arctan 25

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Q: Solve (x² 1 + 2y) dx + (1 - x²) dy = 0; when x = 2, y = 1 1) (x + 1 + 2 ln x 1|) b. (x + 1) y = (x −…

A: Given: x2-1+2ydx + 1-x2dy = 0 , when x=2, y=1. Solve the given differential equation. Concept used:…

Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

Q: [y] + √2x+3] dx = (2x+3)dy, y(-1) = O

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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: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: %3D =D3e %3D 4.

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Q: dy 4x 29. dx 4x + %3D V16 - x2

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Q: 2x-1 3 + If y = Vx2 - x then y' = 3 3 x2-x FO

A: We have given y. We have to identify y' is true or not.

Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

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Q: Refer to the figure below. Find a - b + c. x' = (;+); x0) – 3 X(0) = (G) 4et 7/14 Answer : X = a te?…

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Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

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Q: 6. xydx + 2(x² + 2y²)dy = 0 ; where x = 0, y =1

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Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: implict diff 3). x³ + e5xy - 4y3 = 10

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Q: (b) (12xy2 + 6y + 3e*)dx + (6x²y + 2x)dy = 0

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Q: 3ydx – xdy = 2y4 dy, y(0) = 1 a. (11x – 2y^)3 – 8y = 0 b. (11x – 2y“)3 + 8y = 0 c. (11x +2y“)3 – 8y…

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Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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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

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Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

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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.