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Question: The order of the differential equation whose general solution is given by \(y = \left( C_{1} + C_{2}...

The order of the differential equation whose general solution is given by y=(C1+C2)sin⁡(x+C3)−C4ex+C5y = \left( C_{1} + C_{2} \right)\sin\left( x + C_{3} \right) - C_{4}e^{x + C_{5}}is

A

5

B

4

C

2

D

3

Answer

3

Explanation

Solution

We have, y=(C1+C2)sin⁡(x+C3)−C4ex+C5y = \left( C_{1} + C_{2} \right)\sin\left( x + C_{3} \right) - C_{4}e^{x + C_{5}}

⇒ y=C6sin⁡(x+C3)−C4eC5.ex,whereC6=C1+C2y = C_{6}\sin\left( x + C_{3} \right) - C_{4}e^{C_{5}}.e^{x},whereC_{6} = C_{1} + C_{2}

⇒ y=C6sin⁡(x+C3)−C7ex,whereC4eC5=C7y = C_{6}\sin\left( x + C_{3} \right) - C_{7}e^{x},whereC_{4}e^{C_{5}} = C_{7}Clearly, the above relation contains three arbitrary constants. So, the order of the differential equation satisfying it is 3.