Question
Write the order of the differrntial quation associated with the primitive $\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\text{e}^{-2\text{x}+\text{C}_{4}}$ where $C_1, C_{2,} C_3, C_4$ are arbitrary constants.
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Answer
$\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\text{e}^{-2\text{x}+\text{C}_{4}}$
the given equation can be reduced to:
$\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\big(\text{e}^{-2\text{x}}\times\text{e}^{\text{C}_{4}}\big)$
Here, will be a constant.
We have $3$ constant as $C_1, C_2,$ and $C_3$.
Hence, the order of the differential equation is $3$.
the given equation can be reduced to:
$\text{y}=\text{C}_{1}+\text{C}_{2}\text{e}^{\text{x}}+\text{C}_{3}\big(\text{e}^{-2\text{x}}\times\text{e}^{\text{C}_{4}}\big)$
Here, will be a constant.
We have $3$ constant as $C_1, C_2,$ and $C_3$.
Hence, the order of the differential equation is $3$.
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