The differential equation which represents the family of curves $$y = {c_1}{e^{{c_2}x}},$$ where $${c_1}$$ , and $${c_2}$$ are arbitrary constants, is

The solution of the differential equation

$${{dy} \over {dx}} = {{x + y} \over x}$$ satisfying the condition $$y(1)=1$$ is :

The differential equation of all circles passing through the origin and having their centres on the $$x$$-axis is :

The differential equation whose solution is $$A{x^2} + B{y^2} = 1$$
where $$A$$ and $$B$$ are arbitrary constants is of