Determine which of the following differential equations are linear or nonlinear, separable or not separable. In...

  

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Determine which of the following differential equations are linear or nonlinear, separable or not separable. In each case explain why the differential equation is or is not separable. If separable, find the general solution to the differential equation. Hint: Solution may be not integrable in terms of elementary functions. In this case it can be left in quadrature, i.e. in terms of integral. Don't give up in advance and make sure that this is the case. a) (4+x) dy 2x dx In[(y-2)] b) y' = sin xy+ In c) dy dx = ( 2xycos xIn(y)+4. [20 marks] [5 marks] [20 marks] Determine which of the following differential equations are linear or nonlinear, separable or not separable. In each case explain why the differential equation is or is not separable. If separable, find the general solution to the differential equation. Hint: Solution may be not integrable in terms of elementary functions. In this case it can be left in quadrature, i.e. in terms of integral. Don't give up in advance and make sure that this is the case. a) (4+x) dy 2x dx In[(y-2)] b) y' = sin xy+ In c) dy dx = ( 2xycos xIn(y)+4. [20 marks] [5 marks] [20 marks]