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  4. The order of the differential equation obtained by eliminating arbitrary constants in the family of curves c1y = (c2 +c3 )ex+c4 is

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Q. The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is

KCETKCET 2020

Solution:

$\left(y = [(\frac{C_2 + C_3}{C_1})e^{C_4}]e^x = A e^x,\right)$
where $A = \left((\frac{C_2 + C_3}{C_1})e^{C_4}\right)$
Order = Number of independent arbitrary constants $= 1$