2(a) Given that f (x,y) = 6xy cosx + 5y - siny + 10x, establish...

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2(a) Given that f (x,y) = 6x²y³ – cosx + 5y –- siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. [5marks ] (b) Solve the separable differential equation 7e-3x+2x2-xcosx y' [10marks ] %D -6y3 (c) Solve the IVP x(1 – siny)dy = (cosx – cosy - y)dx. 2 = 0. [10marks ] 2(a) Given that f (x,y) = 6x²y³ – cosx + 5y –- siny + 10x, establish the fact that, the order in which the second order mixed partials derivatives are taken is immaterial. [5marks ] (b) Solve the separable differential equation 7e-3x+2x2-xcosx y' [10marks ] %D -6y3 (c) Solve the IVP x(1 – siny)dy = (cosx – cosy - y)dx. 2 = 0. [10marks ]