Q. 1
1. A thin bar of length \( \pi \) units is placed in boiling water (temperature \( 100^{\circ} \mathrm{C} \) i.e. \( f(x)=100) \). After reaching \( 100^{\circ} \mathrm{C} \) throughout, the bar is moved from the boiling water. With the lateral sides kept insulated, suddenly at \( \mathrm{t}=0 \), the ends are immersed in a medium with constant freezing temperature \( 0^{\circ} \mathrm{C} \). Taking \( C=a=1 \) find the temperature \( u(x, t) \) for \( t>0 \).
