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Homework Statement Find the solution of the equation: α(dy/dt) + y = f(t) for the following conditions: (a) when f(t) = H(t) where H(t) is the Heaviside step function (b) when f(t) = δ(t) where δ(t) is the delta function (c) when f(t) = β^(-1)e^(t/β)H(t) with β<α Homework...

1. Solve the Heat equation u_t = ku_xx for 0 < x < ∏, t > 0 with the initial condition u(x, 0) = 1 + 2sinx and the boundary conditions u(0, t) = u(∏, t) = 1 (Notice that the boundary condition is not homogeneous) 3. Find the solution of the Wave equation u_tt = 4 u_xx with u(0...

Please help me... bump...

Homework Statement Show that if u(x,t) and v(x,t) are solutions to the Dirichlet problems for the Heat equation u_t (x,t) - ku_xx (x,t) = f(x,t), u(x,0) = Φ₁(x), u(0,t) = u(1,t) = g₁(t) v_t (x,t) - kv_xx (x,t) = f(x,t), v(x,0) = Φ₂(x), v(0,t) = v(1,t) = g₂(t) and if Φ₂(x) ≤ Φ₁(x)...