The order of the differential equation whose general solution is given by $y = c_{1} c o s (2 x + c_{2}) - (c_{3} + c_{4}) a^{x + c_{5}} + c_{6} s i n (x - c_{7})$ , is

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Solution

The correct option is C
5

We have $y = c_{1} c o s (2 x + c_{2}) - (c_{3} + c_{4}) a^{x + c_{5}} + c_{6} s i n (x - c_{7})$
$= c_{1} c o s (2 x + c_{2}) - c_{8} . a^{c_{5}} . a^{x} + c_{6} s i n (x - c_{7})$
where $c_{3} + c_{4} = c_{8}$
Since, the above relation contains five arbitrary constants, so the order of the differential equation satisfying it, is 5.

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The order of the differential equation whose general solution is given by y=c1 cos(2x+c2)−(c3+c4)ax+c5+c6sin(x−c7), is

The correct option is C 5 We have y=c1 cos(2x+c2)−(c3+c4)ax+c5+c6sin(x−c7) =c1 cos(2x+c2)−c8.ac5.ax+c6 sin(x−c7) where c3+c4=c8 Since, the above relation contains five arbitrary constants, so the order of the differential equation satisfying it, is 5.

The order of the differential equation whose general solution is given by $y = c_{1} c o s (2 x + c_{2}) - (c_{3} + c_{4}) a^{x + c_{5}} + c_{6} s i n (x - c_{7})$ , is