The order of the differential equation whose general solution is given by
y = c₁ cos (2x + c₂) − (c₃ + c₄) a^x^{+ c₅} + c₆ sin (x − c₇) is
(a) 3
(b) 4
(c) 5
(d) 2

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Solution

(c) 5

The given equation can be reduced to : $y = c_{1} \cos (2 x + c_{2}) - (c) a^{x} \times a^{c_{5}} + c_{6} \sin (x - c_{7}) where c = c_{3} + c_{4} a n d a^{c_{5}} will be a constant$

There are 5 constants $(c_{1}, c_{2,} c, c_{6}, c_{7})$ in the given differential equation.
Hence, the order of the differential equation 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 + c6 sin (x − c7) is (a) 3 (b) 4 (c) 5 (d) 2

(c) 5 The given equation can be reduced to : y=c1cos(2x+c2)-(c)ax×ac5+c6sin(x-c7)where c=c3+c4 and ac5 will be a constant There are 5 constants(c1, c2, c, c6, c7) in the given differential equation. Hence, the order of the differential equation is 5.

The order of the differential equation whose general solution is given by
y = c₁ cos (2x + c₂) − (c₃ + c₄) a^x^{+ c₅} + c₆ sin (x − c₇) is
(a) 3
(b) 4
(c) 5
(d) 2