The order of the differential equation associated with the primitive y=c1+c2 ex+c3 e-2 x+c4, where c1, c2, c3, c4 are arbitrary constants, is

Question

The order of the differential equation associated with the primitive y=c1+c2 ex+c3 e-2 x+c4, where c1, c2, c3, c4 are arbitrary constants, is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We have, y=c1+c2 ex+c3 e-2 x+c4 ⇒ y=c1+c2 ex+c3 e-2 x ⋅ ec4 ⇒ y=c1+c2 ex+c3'e-2 x, where c3'=c3 ec4 It is an equation containing three arbitrary constants. So, the associated differential equation is of order 3 .

Q. The order of the differential equation associated with the primitive y=c1​+c2​ex+c3​e−2x+c4​, where c1​,c2​,c3​,c4​ are arbitrary constants, is ____

We have, y=c1​+c2​ex+c3​e−2x+c4​ ⇒y=c1​+c2​ex+c3​e−2x⋅ec4​ ⇒y=c1​+c2​ex+c3′​e−2x, where c3′​=c3​ec4​ It is an equation containing three arbitrary constants. So, the associated differential equation is of order 3.

Q. The order of the differential equation associated with the primitive $y = c_{1} + c_{2} e^{x} + c_{3} e^{- 2 x + c_{4}},$ where $c_{1}, c_{2}, c_{3}, c_{4}$ are arbitrary constants, is ____