The order of the differential equation whose solution is $a e^{x} + b e^{2x} + c e^{3x} + d = 0$ is:

The differential equation having $y=(a+b) e^{cx+d}$ as its general solution,where $a, b, c, d$ are arbitrary constants,is

The differential equation of the family of lines having $x$-intercept $a$ and $y$-intercept $b$ is

If $m$ and $n$ are the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis, then $m n-m+n=$

Form the differential equation of the family of circles in the first quadrant which touch the coordinate axes.

The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants will be: