The solution of the differential equation $${{dy} \over {dx}} + {y \over x} = x$$ with the condition that $$y=1$$ at $$x=1$$ is

The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \right)}^3} + {y^2}} = 0$$ are respectively

The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \over {\partial x}},q = {{\partial z} \over {\partial y}}} \right)\,\,$$

Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of