The order of the differential equation whose general solution is given by $y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5})$ is

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Solution

The correct option is B 4
$y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5}) = C_{1} . e^{C_{2}} e^{2 x} + C_{3} e^{x} + C_{4} (s i n x c o s C_{5} + c o s x s i n C_{5}) = A e^{2 x} + C_{3} e^{x} + B s i n x + D c o s x$
Here, $A = C_{1} e^{C_{2}}, B = C_{4} c o s C_{5}, D = C_{4} s i n C_{5}$
(Since equation consists of four arbitrary constants)
$∴$ order of differential equation = 4.

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