2. Solve of the following boundary-value problem by the method of separation of variables. du = 4 u(0,t) = 0, u(n,t) = 0, u(x,0) = 2 Sin 3x - 4 Sin 5x. 3. f(x) function has a 2n period and given f(x) = 1, for -n

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A:

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A:

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A: Given initial value problem can be evaluated as shown below by using substitution method

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A: See the attachment.

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A: Below is the answer

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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.