UTM UTM QUESTION 3 (20 MARKS) a) Use the d'Alembert solution to solve UTM UTM UTM & UTM UTM &UTM TM UTM 3 UTM TM UTM J²u

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Utm Utm Question 3 20 Marks A Use The D Alembert Solution To Solve Utm Utm Utm Utm Utm Utm Tm Utm 3 Utm Tm Utm J U 1 (79.79 KiB) Viewed 87 times

UTM UTM QUESTION 3 (20 MARKS) a) Use the d'Alembert solution to solve UTM UTM UTM & UTM UTM &UTM TM UTM 3 UTM TM UTM J²u 18²2 21² 90x² UTM UTM (,0) = with boundary conditions UTM UTM &UTMUSCE 1793 UTM & UTM & UTM and initial condition -∞0 < x <∞0, t≥ 0, cos²x, u(x, 0) = e*+¹. b) Solve the following heat equation by using the method of separation of variables TM & UTS 3 UTM & UTM UT du J²u = 2 dt 0x²¹ UTM UTM UTM UTM CCM * UTM 0≤x≤3, t≥ 0, u(0,t)=0, u(3, t) = 0, t≥0, UTM UTM 3 UTM 5 UT (5 marks)TM UT u(x,0)=2+, 0≤x≤3. UTMUT 5 UTM & UT (15 marks)