3. A uniform rod of length 10 meters is held at both ends. The temperature u(x, t) at any time t of a point P which is r distance away from any of the two endpoints is du a?u 0 0, subject to u(0, t) = 0 u(10, t) = 0 u(x, 0) = 2 – x. Use the method of separation variables to show that the general solution is given by u(x, t) = bn sin 10 n=1 where 4 bn (1+4(-1)"), n = 1,2, 3, ...

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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.