a²u ax for the condition of heat along a rod of length ? subject to du Solve the equation at following condition (i) u is not infinity for t 00 au (ii) for x=0 and x= ! for any time t. (iii) u = lx – x² for t=0 between x=0 and x= ? .

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A: Consider the provided question,

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Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: dy 64). y(ln 4) = 0 31S = 3 e 3tsin (e 3t - dt The solution is y=

A: Integration both side and applying initial conditions then we can find its solution

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Q: 3. A particle starts at rest on a smooth inclined plane. At the end of t seconds, the position of…

A: Please refer the attached image for complete solution

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Q: 6. An object is dropped from the top of a building 200 m high. The object encounters air resistance…

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Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 lb/gal…

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Q: Q: Using Euler's method, find yus for the initial value problem y' = 2x+cos(x), y (0) = 1. h=2.65

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Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Given the length of the thin bar L=3m with one at x=0 and the other end at x=3 The thermal…

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Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e3 – x…

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Q: (i) A business manager determines that t months after production begins on a new product, the number…

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Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: A thin bar of length L 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Consider the provided question,

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

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Q: Solve the initial value problem for y as a function of x. (x? + 256) = 23, y(16 3) = 0 dx The…

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Q: Do not use a calculator for this problem. Find the x-value where the relative maximum of y = e3…

A: Given: y=ex3-x2 we have given first guess x1=0 Using Newton's method: xn+1=xn-fxnf'xn…

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Q: Q1): The concentration of salt is given as a function of time by: dx = 37.5-3.5x di at the initial…

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Q: A falling object satisfies the initial value problem dv 9.8 | dt -(), v (0) = 0 where v is the…

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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.