QUESTION TWO Solve the following pde's by the operator method. (i) Uxxx - 2Uxxy = 2ex...

 

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QUESTION TWO Solve the following pde's by the operator method. (i) Uxxx - 2Uxxy = 2e²x + 3x²y (ii) Uxx + Uxy - 6Uyy = y cos x [8 Marks] [7 Marks] QUESTION THREE (a) Given the pde Uxx = U₁,U(x,0)=x² (25-x². Solve the pde by the method of separation of variables. [6 Marks] (b) A string is stretched and fastened to two point < apart. Motion is started by displacing the spring from which it is released at a time t = 0. Find the displacement at any point at a distance x from one end at time t, given that the equation of vibration of the string is Utt = c²Uxx under the following conditions; [9 Marks] (i) U(0, t) = 0 (ii) U(0, x) = 0 (iii) (U(l, t) = 0, (iv) U(x, 0) = 10 sin "x QUESTION TWO Solve the following pde's by the operator method. (i) Uxxx - 2Uxxy = 2e²x + 3x²y (ii) Uxx + Uxy - 6Uyy = y cos x [8 Marks] [7 Marks] QUESTION THREE (a) Given the pde Uxx = U₁,U(x,0)=x² (25-x². Solve the pde by the method of separation of variables. [6 Marks] (b) A string is stretched and fastened to two point < apart. Motion is started by displacing the spring from which it is released at a time t = 0. Find the displacement at any point at a distance x from one end at time t, given that the equation of vibration of the string is Utt = c²Uxx under the following conditions; [9 Marks] (i) U(0, t) = 0 (ii) U(0, x) = 0 (iii) (U(l, t) = 0, (iv) U(x, 0) = 10 sin "x

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The operator method is a method used to solve partial differential equations PDEs by constructing the characteristic equation which is the equation formed by equating the coefficients of the independe... View the full answer