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Differential Equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
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 C1, C2, C3, C4 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 C1, C2, and C3.
Hence, the order of the differential equation is 3.

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