Applying separation of variables to the PDE U-+2u,=0, produces the following ODES. XX O a X'+2X-cX=0, and T-cT=0. O b. X" +2X- cX = 0, and T-CT=0. Oc. X'-2X -oX=0, and T' -CT=0. O d. 2X"+X – cX= 0, and T-CT=0. O e. 2X-X - cX = 0, and T-CT=0. O f. X"-2X-cX 0, and T-CT= 0.

Q: (4) (2.1×10)×(0.38)-(2.1x03) 10

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Q: 6. Evaluate when; x = -1 x3-5x²+x² II

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Q: x + 3 a. Given that f(x) + x*, write an expression to represent each of the following. 7 i. f(u + v)…

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Q: ine x and y such that -4 3 0 -4 + -3 x - y -1 -2 4 -4 3 2x + y

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Q: Lim (x-2x) X>-1

A: Limit of a function at a point is the value the function tends to as we approach that point. Limit…

Q: 1 t² √9t² - 1 dt

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Q: 6x + 5 > -2(x – 3) – 25

A: 6x + 5 > -2(x-3) - 25 6x + 5 > -2x + 6 - 25 Add (2x) on both side 8x + 5 > -19

Q: For fx) = x+6, find each of the following a. (-1) e. (for xs97) (5) a. f-1)-5 b.r (5)-0

A: Given query is to find the indicated valen do the function.

Q: Add and simplify. 2x X+ X +1 2x2 X +1 X(x +3) X+1 3x X +1 4 x +1 X+1

A: Using cross multiplication & simplification

Q: Find and simplify the difference quotient f(x)=x² + 4x-5 OA. 2x+h-5 2x²+2x+2xh+h²+h-10 h OB. OC. 1…

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Q: Find (f + g)(x)

A: we have to apply composition property to solve given function please note: we are only supposed to…

Q: Simplify. 2 [5x 5y2 0]

A: We need to simplify the given expression.

Q: Divide: -3+4x-x -7x+12 -6x+5 x-8x+15

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Q: Compute and simplify the difference quotient: f(x +h)-f(x) h 15x 7h + 14 - h = 0. 10x² + 5h+ 7x 10x…

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Q: Question 7 Translate the following statement into symbols. Marsha finished the sign, or the table…

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Q: Express x XOR y with only AND, OR and NOT.

A: We can write-                    x OR y = NOT (  NOT x   AND   NOT y )

Q: 6. Determine the domain of the following: a. y = -3/14 + 3x b. y = V4 + 3x –- x² x+1 С. у %3 х(х-2)…

A: Domain of given function at which y(x) is defined.

Q: Evaluate xe dp- X6 (x +1)*

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Q: Evaluate. Use a capital C for any constant. fae 9 /6(82 – 1)(82² – 2æ + 3)° dæ (3(8x^2-2x+3)^10)/8 -

A: NOTE: Refresh your page if you can't see any equations. . ...............(1)

Q: .2 ペ+15X+ 32X"+23x*+25K-3 Ax (+メ+2) (x2+1)。 2.

A: ∫x6+7x5+15x4+32x3+23x2+25x-3x2+x+22x2+12dx

Q: If f(x) = x2 – 6x and g(x) = 6 – x³, evaluate the following. %3D a. (f+ g)(- 2) b. (g - )(- 4) c. (f…

A: The given functions are f(x)=x2-6x  &  g(x)=6-x3

Q: d da Compute (10-3x)*.

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Q: For f(x) = 5x - 3 and g(x) = 2x2 – 5, find the following functions. a. (fo g)(x); b. (g o f)(x); c.…

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Q: The set D = {x +4y - 22 0} is the domain of which of the following functions? In (2x? + 8y? - 3) 2.…

A: We have to find domain

Q: Find the equation of (x) = 5* + 2 after it has been shifted up 4 units. O Ax) = 5*+4+ 2 O f(x) = 5*…

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Q: Integrate the following x2(x-4)ex(x-2)

A: find out the integral of x2(x-4)exx-2

Q: Add. x+1 X + 2 +52 x²+4x-5 x²-1 x(x-1) 2x+1 x(x-1) 2x²-1 x(x-1) x²+3x+1 x(x-1)

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Q: For each ODE with non-constant coefficients, use the given homogenous solution to find a particular…

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Q: (9) y 2*+2 4 15 (11) y: (

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Q: Q.2 a. Find the Domain for y- /4 -x +

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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.