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Also I need DETAILED STEP BY STEP solutions, do not writesimplified. Thank you!!
Soalan 4 Question 4 (a) (b) (c) Selesaikan penyelesaian am PDE yang mewakili masalah haba. Solve the PDE's general solution which represents the heat problem. di mana u(x, t) = fungsi suhu where u(x, t) = temperature function. Pu dr dx|x=3 Utotal = 5 d²u dr² (10 markah/marks) Diberikan = 0, u(0,t)=0 untuk t > 0, dan u(x,0)= 30 untuk 0<x<3. Pertimbangkan syarat sempadan untuk kes 3 (A = α²) sahaja dan sahkan: Given = 0. u(0.t)=0 fort >0.and u(x.0)= 30 for 0<x<3. Consider the boundary condition for case 3 (A=a2) only and verify that. x1x=3 = 0 Σ e-s((2n-1)²)* t (B₁nsin((2n − 1) 77 x)) - n=1 Nota: Andaikan kes 1 (A=0) dan kes 2 (A=a2) mempunyai penyelesaian khusus sifar di mana a > 0. Petunjuk: cos s[(2n-1)] = 0, di mana n = 1,2,3,... Note: Assume case 1 (A=0) and case 2 (A=-- a²) have zero particular solution where a> 0. Hint: cos s[(2n-1)] = 0, where n = 1,2,3,... (4 markah/marks) Dengan menggunakan syarat awal untuk penyelesaian khusus di bahagian (b), kita memperoleh -1 (B3nsin((2n-1)=x)) = 30. Diberikan B3n = S f(x) sin(Cx) dx, tentukan koefisien L, t. f(x) dan C sahaja tanpa menyelesaikan pengamiran. En=1 (Bansin((2n-1) ² x)) = = 30. Given By using the initial condition on the particular solution in part (b) we obtain f(x) sin(Cx) dx, determine B3n = coefficients L. T. f(x) and C only without so the integration. (1 markah/mark)
It is better to type down your answer, if not, please write nicely. Also I need DETAILED STEP BY STEP solutions, do not
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