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

A:

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

A:

Q: 51+* + 1 y = 5*

A: Given: y=51+x+15x     ⇒   y=51+x5x + 15x                =5+ 15x       y-5=15x           5x=1y-5   x…

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: I (Inx)³ nx-X

A: Let u and v be the function of x  Then∫uvdx=u∫vdx-∫(dudx∫vdx)dx

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Find x and y such that,  77815x - 8216y=(77815 , 8216

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Q: b) (9x²-6x+26) *

A:

Q: y = ae-2r + e-2r bxe

A:

Q: Find the slope: O 4/3 O 3/4 O 4/3 O o O O

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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: exp(x) = ex ?  Is it just a matter of notation, or does exp( ) mean something else?

A: Yes this is true exp(x) = e^x  exp(x) is command in coding language to type e^x

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

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Q: y d²y = sin y. dr2 Y d'y dr2 d'y Ne dx2 7 -y=1 1 -1=Y У

A: As we know that; The standard form of the linear ordinary differential equation is:…

Q: None

A: Step 1: Step 2: Step 3: Step 4:

Q: 3) f = {(0, a), (1, d), (5, e), (9, c)} find the inverse of this function.

A:

Q: . Determine if y is a function of x in x = y? + 5.

A: Given equation - x = y2+5Let's solve for y =- y2 = x-5y = x-5       ........(1)

Q: Solve the non-linear Differential Equation y"=-e xy = f(x) by explicitly following these steps:…

A: Use the following formulae, to obtain the solution.

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: Which of the following functions has an inverse? xlxl (a) x³ + x - 1, (b) x³ - x + 1, (C)- x+1 - (d)…

A: (a) fx=x3+x-1 If no horizontal line intersects the graph of f more than once, then f does have an…

Q: Evaluate 00 x²dx 1 – 2cos20 x² + x4 -00 where 0 < 0 <T/2. Please also make comments.

A: We can solve this integral by integration method

Q: Write the following function in the form a + ib

A: Answer

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

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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.