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SOLVED: For partial derivatives of a function, use the subscript notation. So, for the second partial derivative of the function u(x, t) with respect to x, use uxx. For ordinary differential equations, use the prime notation. So, the second derivative of the function f(x) can be written as f”(x).Solve the heat equation:0*u 6 = 0120 0u(0, t) = 92, u(4, t) = 85, t > 0u(x, 0) = 4 - x, 0 0v(0, t) = 0, v(4, t) = 0, t > 0v(x, 0) = 4 - x - S(x), 0 < x < 4Using the substitution u = v S, we have:0^