CONFIDENTIAL Q1 (a) (2 (b) (c) (a) Show that y = Ae* + Be, where A and B are constants, is the general solution of the d

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Confidential Q1 A 2 B C A Show That Y Ae Be Where A And B Are Constants Is The General Solution Of The D 1 (57.68 KiB) Viewed 32 times

CONFIDENTIAL Q1 (a) (2 (b) (c) (a) Show that y = Ae* + Be, where A and B are constants, is the general solution of the differential equation "+'-6y=0. Hence, find the solution when (1) = 2e²e³ and y(0) = 1. (5 marks) By using the substitution z = cos y, show that the differential equation can be reduce to (i) (i) Hence, solve the original equation when y(1) = 0. (ii) y BNJ12303 BNQ10603 A ENP12303/BNT 12303/BNR17903 d'y 4245 (iii) x² is an exact equation. dy coty dx X Show that the equation (3x²²-10xy²)dx + (2x³-10x²y)dy = 0 (3 marks) (ii) Then, determine the general solution from the given differential equation. (7 marks) dz² For each of the equation, determine whether it is linear or not? If not, give the reason. If yes, show that the equation is homogeneous and state its coefficient form. d²y dr.² dee dz dx x dx +10y=0 = 6²³ csc y Z = -²¹. -3y=3x² +2x+y=0 de (10 marks) 2 (2 marks) (2 marks) (2 marks) CONFIDENTIAL