2 A 3 cm length silver bar with a constant cross section area 1 cm² (density 10 g/cm³, thermal conductivity 3 cal/(cm sec °C), specific heat 0.15 cal/(g °C)), is perfectly insulated laterally, with ends kept at temperature 0 °C and initial uniform temperature f(x) =25 °C. The heat equation is: 1 ди ax c? at (a) Show that c? = 2. (b) By using the method of separation of variable, and applying the boundary condition, prove that 2nx³t u(x,t) -Σ, sin: NTX -e 3 9 n=1 where b, is an arbitrary constant. (c) By applying the initial condition, find the value of b,.

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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.