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. - Mathematics

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.

Solution

$y = C_{1} + C_{2} e^{x} + C_{3} e^{- 2 x + C_{4}}$
the given equation can be reduced to:
$y = C_{1} + C_{2} e^{x} + C_{3} (e^{- 2 x} \times e^{c_{4}})$
$Here, e^{c_{4}} will be a constant .$
$We have 3 constants as C_{1}, C_{2} and C_{3} .$
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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General and Particular Solutions of a Differential Equation

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Chapter 22: Differential Equations - Very Short Answers [Page 138]

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Chapter 22 Differential Equations
Very Short Answers | Q 16 | Page 138

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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. - Mathematics

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