Answer to Question #297056 in Differential Equations for Roma

Question

<e> a) A rod of length 𝐿 has its ends 𝐴 and 𝐵 maintained at 20 °𝐶 and 40 °𝐶 respectively

until steady state condition prevail. The temperature at 𝐴 is suddenly raised to

50 °𝐶 while that at 𝐵 is lowered to 10 °𝐶 and maintained thereafter. Find the

subsequent temperature distribution of the rod.

b) Solve (𝑥

2 − 𝑦

2 − 𝑧

2

)𝑝 + (2𝑥𝑦) 𝑞 = 2𝑥𝑧 where 𝑝 =

𝜕𝑧

𝜕𝑥 , 𝑞 =

𝜕𝑧

𝜕𝑦