Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t> 0. Find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that 2 = 1. u(x, 0) = 30, 0

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

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Q: For the function f(x) = In x 11x find f''(x). Then find f''(0) and f''(6).

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Q: Wave mechanics are often employed for

A: Given,              ∂2u∂t2=16∂2u∂t2  for all  0≤x≤10 and t≥0.             ...(1)

Q: 3. Find the derivative dy/dx of each implicit function in sub-items 3.1 and 3.2: 3.1. F(x, y) = x² +…

A: 1) F(x,y)=x2+y2+xy=0 2) F(x,y)=x3+x2y+y3=0

Q: Assume f(3) = 0, f'(3) = 6, g(3) = 1, and g'(3) = 3 f(x) g(x)* Find h'(3) given h(x) = A. -2 B. 2/2…

A: Given,

Q: Suppose the volume of a tree is given by V=1c²h where c is the circumference of the tree in meters…

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Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx (2-x), 0<x <3 f(x) = 0,…

A: Given : The pdf of random variable x is : f(x)=Kx2(2-x),0,x&lt;30,elsewhere We want to find value of…

Q: length, is given by the heat equation, ди 2²u əx² Ət (0 0), here x measures distance along the bar,…

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Q: Compute f(s), where f(x) = cos oz and 8 >

A: We have to find out the Laplace transformation of f(x) = cos

Q: 3. Let X be the amount of an insurance claim which has following pdf: Kx2(2-x), 0<x <3 0 <x f(x) =-…

A: It is given that, x be the amount of claim with pdf fx = Kx2 2-x,0&lt;x&lt;30,elsewhere

Q: 5. A tank contains 100 gal of water and 50 lbs of salt. Water containing a salt concentration of (1…

A: (a)Given that a tank contains 100 gal of water, and 50 lbs of salt.The water with the salt flows in…

Q: Let h(x) = If f(2) = 1 and f'(2) = -1, find h'(2). A B C OD E A. 36 B. 27 C. 12 D. -12 E. 48

A: Step 1:To solve the problem, let's break it down step by step.Given the function:h(x)=[f(x)x​]3We…

Q: Fihd f if f"(±) = sin(z), f(0) = -1, f'(0) = -1, f"(0) = -4. %3D f(z) =| D

A: Given: f'''(x)=sin(x),  f(0)=-1,  f'(0)=-1,  f"(0)=-4

Q: ex+1 b) Find f'(x) of f (x) = x2+3 %3D c) For y = xk+1, where k is a constant. Find y'".

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Q: 4. A graph of a function y = f(t) is shown below. Use this graph to answer the following questions…

A: We will use If f(x) is a function. Then roots of f'(x) is called critical points and if f'(a)=0.…

Q: Q/ if fx(x)= x and (g) is function of R.V X find the PDF of g(x)= X² ?

A: # Given: pdf of random variable x is f(x)=x  then to find pdf of y=x^2 ?

Q: Let f(r) = 2 sec(2r). Determine the following %3D f'(x) = 4 sec(2x) tan(2x) %3D f'(4) =

A: As we know that; The chain rule: fgx'=f'gx·g'x And ddxsecx=secxtanx From the given function:…

Q: dy dt 7=2 €²-1 b) y (₁)=2 b) y(-1)=2 (c) y(₁) =3 d) y (0) = 2 Seproble method e) stote, which for…

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Q: Let z = x"y . If x increases by 2% and y increases by 3% then using partial differentiation theory…

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Q: • Let f (x) = cos(x). Use central-difference formula of order 0(h²) with step size h 0.1 , 0.01 ,…

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Q: A function f(x) has an inflection point at (1,8). Which of the following could have been the result…

A: A necessary condition for x to be an inflection point is f''(x)=0. A sufficient condition requires…

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

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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.