Q1 (a) (b) (c) -3x Show that y = Ae²* + Be ³*, where A and B are constants, is the general solution of the differential

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Q1 A B C 3x Show That Y Ae Be Where A And B Are Constants Is The General Solution Of The Differential 1 (84.08 KiB) Viewed 32 times

Q1 (a) (b) (c) -3x Show that y = Ae²* + Be ³*, where A and B are constants, is the general solution of the differential equation y"+y'-6y=0. Hence, find the solution when y(1) = 2e²-e³ and y(0) = 1. By using the substitution z = cos y, show that the differential equation dy cot y 3x dx X can be reduce to dz dx x Hence, solve the original equation when y(1) = 0. (i) = e csc y (ii) = -e³x. Show that the equation (3x²y² - 10xy²)dx + (2x³y - 10x²y)dy = 0 is an exact equation. (5 marks) (10 marks) (3 marks) Then, determine the general solution from the given differential equation. (7 marks)