The order of the differential equation whose general solution is given by $y = (c_{1} + c_{2}) c o s (x + c_{3}) - c_{4} . e^{x + c_{s}}$ is

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Solution

The correct option is B 3
$y = (c_{1} + c_{2}) c o s (x + c_{3}) - c_{4} . e^{c 5} . e^{x}$
$L e t c_{1} + c_{2} = A a n d c_{3} = B, c_{4} . e^{c 5} = C$
$∴ y = A c o s (X + B) - C e^{x}$
3 arbitrary constants $\Rightarrow$ order = 3
Actual equation after solving is $\frac{d^{3} y}{d x^{3}} + \frac{d y}{d x} = \frac{d^{2} y}{d x^{2}} + y$

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