Consider the ODE written in differential form + {4 (12 x + 5) cos(2y)}dx+{-8 (6.22 + 5 x ) sin(2y)} dy=0 (a) The express

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Consider The Ode Written In Differential Form 4 12 X 5 Cos 2y Dx 8 6 22 5 X Sin 2y Dy 0 A The Express 1 (132.55 KiB) Viewed 27 times

Consider the ODE written in differential form + {4 (12 x + 5) cos(2y)}dx+{-8 (6.22 + 5 x ) sin(2y)} dy=0 (a) The expression for the test of exactness is My = No = O 4 (6 22 +50) cos(24) (622 +52 +5x) sin(2y) 0-8 0-8 (122+5) sin(2y) 04 (12x+5) cos(2y) The implicit solution to the ODE, u(x,y) = c, can be found by solving a system of two PDEs. (b) What is the expression for ux? 0 -8 (6 r2 + 5x ) sin(2y) 0-8 (12x+5) sin(2y) O 4 (6r2 +5 2 ) cos(24) 04 (122+5) cos(2 y) 4 + 0-8 (c) What is the expression for uy? O-8 (12x + 5) sin(2y) (6 x2 + 5x ) sin(2y) 04 (12x+5) cos(2 y) O 4 (6 x2 +50) cos(23) + (d) The implicit solution is O 4 (6x2 + 5 x ) cos(2 y)=C O 4 (12x+5) cos(2 y) = C 0-8 (12x+5) sin(2 y) = C 0-8 (6.22 +5 x) sin(2y)=c where c is an arbitrary constant. The following hint maybe helpful in some instances (i.e. your individually randomised problem): If u(x,y) = c then u(x, y) +k= c is also a solution, where he is a constant.