A lumped mass of m 35 kg with the initial temperature of To 2000 K radiates and convects heat from its surface of A = 1.5 m² to a medium at the temperature of T₁ = 100 K. The lumped transient temperature response T that varies with time t is determined from the ordinary differential equation dT dt εσ Α + (TT) + hA (T-Ta) = 0 mc mC (1) where = 0.7 is the surface emissivity, σ = 5.67×10-8 J/sec-m²-K4 is the Stefan- Boltzmann constant, and c= 445 J/kg-K is the specific heat of the lumped mass, and h= 50 W/m²-K is the convective heat transfer coefficient. (a) Use the Euler, modified Euler, and Heun's methods to calculate the transient temperature T(t) from t = 0 to 100 sec. Plot the results from all three methods on the same graph. (b) Apply finite difference (backward, forward, and central) to the solution obtained in part (a). Compare the finite difference results with the original ODE by plotting both sets of data. Present three separate graphs to compare the solutions from Euler, modified Euler, and Heun's methods.