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

Question

Dr. Abubacker · Accepted Answer

(c)
$y = \left( c_{1} + c_{2} ight)\cos{\left( x + c_{3} ight) - c_{4}e^{x + c_{5}}}$
$y_{1} = - \left( c_{1} + c_{2} ight)\sin{\left( x + c_{3} ight) - c_{4}}e^{x + c_{5}}$
$y_{2} = - \left( c_{1} + c_{2} ight)\cos{\left( x + c_{3} ight) - c_{4}}e^{x + c_{5}} = - y - 2c_{4}e^{x + c_{5}}$
$y_{3} = - y_{1} - 2c_{4}e^{x + c_{5}}$
$y_{3} = - y_{1} + y_{2} - y$
$	herefore$ Differential equation is
$y_{3} - y_{2} + y_{1} - y = 0$
Which is order 3

Q. The order of the differential equation whose general solution is given by $y = \left( c_{1} + c_{2} \right)\cos{\left( x + c_{3} \right) - c_{4}e^{x + c_{5}}}$ where $c_{1},c_{2},c_{3},c_{4}and\ c_{5}$ are arbitrary constants is

Explanation

Reviewed by Dr. Abubacker

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