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.

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Solution

$y = C_{1} + C_{2} e^{x} + C_{3} e^{- 2 x + C_{4}} the given equation can be reduced to : y = C_{1} + C_{2} e^{x} + C_{3} (e^{- 2 x} \times e^{c_{4}}) Here, e^{c_{4}} w ill be a constant . W e h a v e 3 c o n s \tan t s a s C_{1}, C_{2} a n d C_{3} . and a differential equation of order n always contains exactly n essential arbitrary constants . Hence, the order of the required differntial equation is 3 .$

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Find the order of the differential equation

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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.

y=C1+C2ex+C3e-2x+C4the given equation can be reduced to:y=C1+C2ex+C3(e-2x×ec4)Here, ec4 will be a constant.We have 3 constants as C1, C2 and C3.and a differential equation of order n always contains exactly n essential arbitrary constants.Hence, the order of the required differntial equation is 3.

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.