The second-order differential equation in an unknown function $$u : u(x, y)$$ is defined as $$\frac{\partial^2 u}{\partial x^2}= 2$$

Assuming $$g : g(x)$$, $$f : f(y)$$, and $$h : h(y)$$, the general solution of the above differential equation is

The steady-state temperature distribution in a square plate ABCD is governed by the 2-dimensional Laplace equation. The side AB is kept at a temperature of 100°C and the other three sides are kept at a temperature of 0°C. Ignoring the effect of discontinuities in the boundary conditions at the corners, the steady-state temperature at the center of the plate is obtained as T₀°C. Due to symmetry, the steady-state temperature at the center will be same (T₀°C), when any one side of the square is kept at a temperature of 100°C and the remaining three sides are kept at a temperature of 0°C. Using the principle of superposition, the value of T₀ is _________ (rounded off to two decimal places).