First slide

Introduction to Differential equations

Question

The order of the differential equation whose general solution is given by $y = (C_{1} + C_{2}) \cos (x + C_{3}) - C_{4} e^{x + C_{5}}$
where $C_{1}, C_{2}, C_{2}, C_{4}, C_{5}$ are arbitrary constant is

Moderate

Solution

Since $C_{1} + C_{2}$ is one constant $C_{4} e^{x + C_{5}}$
$= C_{1} e^{C_{5}} e^{x}$
Thus there are three arbitrary constants. So the order of the differential equation is 3.

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