The solution of $${{dy} \over {dx}} = {y \over x} + \tan {y \over x}$$ is

Integrating factor (I.F.) of the differential equation $${{dy} \over {dx}} - {{3{x^2}} \over {1 + {x^3}}}y = {{{{\sin }^2}x} \over {1 + x}}$$ is

The differential equation of y = ae^bx (a & b are parameters) is

If $$y = {x \over {{{\log }_e}|cx|}}$$ is the solution of the differential equation $${{dy} \over {dx}} = {y \over x} + \phi \left( {{x \over y}} \right)$$, then $$\phi \left( {{x \over y}} \right)$$ is given by