A pipe is made of a material, the thermal conductivity of which is simultaneously dependent on radius and temperature, such that k = 0.01t/r, where the radius is in metres and t is expressed in degrees Celsius. The pipe has inner and outer radii r1 = 0.1 m and r2 = 0.2 m, with corresponding surface temperatures of t1 = 30 degC and t2 = 20 degC respectively. Determine the equation of the temperature field within the pipe material.