हिंदी

Write 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.

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प्रश्न

Write 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.

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उत्तर

\[y = C_1 + C_2 e^x + C_3 e^{- 2x + C_4} \]
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 .

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अध्याय 21: Differential Equations - Very Short Answers [पृष्ठ १३८]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 21 Differential Equations
Very Short Answers | Q 16 | पृष्ठ १३८

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