A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x,y) denote the temperature satisfying the equation a²u + əx² ' əy² a²u = 0. Find the steady state temperature u(x, y), by assuming the solution to be of the form и (х, у) %3D (Аерх + Be-рж)(С сos pу + D sin py).

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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.