Question

Write the order of the differential equation associated with the primitive y = C₁ + C₂ e^x + C₃ e^{−2x + C₄}, where C₁, C₂, C₃, C₄ are arbitrary constants.

Answer 1

\[y = C_1 + C_2 e^x + C_3 e^{- 2x + C_4} \]
the given equation can be reduced to: 
\[y = C_1 + C_2 e^x + C_3 ( e^{- 2x} \times e^{c_4} )\]
\[\text{ Here, }e^{c_4}\text{ will be a constant .} \]
\[\text{ We have 3 constants as }C_1 , C_2\text{ and }C_3 . \]
and a differential equation of order n always contains exactly n essential arbitrary constants .
Hence, the order of the required differntial equation is 3 .