Midsemester test Rei Consider the ODE written in differential form {18 cosh(87) (172 +2y)} dx + (6 sinh(87) (8y + 2)} dy

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Midsemester Test Rei Consider The Ode Written In Differential Form 18 Cosh 87 172 2y Dx 6 Sinh 87 8y 2 Dy 1 (168.4 KiB) Viewed 33 times

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Midsemester test Rei Consider the ODE written in differential form {18 cosh(87) (172 +2y)} dx + (6 sinh(87) (8y + 2)} dy=0 (a) The expression for the test of exactness is My=N; 48 cosh(81)(8y+2) 0 6 sinh(85) (8 g+ 2) O 6 sinh(84)(4x2 + 2y) 48 cosh(83) (472 +2y) + The implicit solution to the ODE, u(z,y) = can be found by solving a system of two PDEs. (b) What is the expression for u? 0 6 sinh(85) (8 g+ 2) 48 cosh(82) (472 +2y) O 6 sinh(85) (4x2 + 2y) 48 cosh(81) (8y + 2) (c) What is the expression for ty? Ô sinh(85) (4x2 + 2 -2y) O 48 cosh(8.1) (4y2 + 2y) 0 6 sinh(85) (8 + 2) O 48 cosh(8.c) (8y+2) (d) The implicit solution is O 48 cosh(8r) (8y+2) = 0 0 6 sinh(85) (8 y+2) = 0 0 48 cosh(8.-) ( 4y2 + 2y) O 6 sinh(85) (4,2 + 2 )=c + C where c is an arbitrary constant. Su