I analysed the thermal behaviour of a metal plate (lying on an insulating surface) when the sun shines on it. I obtained a differential equation that I don't know how to solve. So the problem: The flux density solar radiation onto the plate varies throughout the day as $$ j=j_{\ast} \cdot \sin((\frac{t}{t_0}\pi) $$ Where $t_0$ is the length of the day and $j_*=1361\frac{W}{m^2}$ is the solar constant. The heat transfer inside the plate is very fast - the temperature is always the same at all points inside the plate. The thickness of the plate is $h$, the product of its density and specific heat capacity will be denoted by $C=c_{spec}\cdot \rho$. The starting temperature (in the morning) is $T_0$ and the Stefan-Boltzmann constant is $\sigma$. The plate only radiates on one side and only absorbs radiation on that same side. What I obtained is: $$ dT=\frac{1}{hC}(j_*\sin(\frac{t}{t_0}\pi)-\sigma T^4) dt $$ Is this analytically solvable? If yes, how? If not, what approximation technique would yield the best results?
Thank you for your answers