The order of the differential equation whose general solution is given by y=(C1+C2)cos(x+C3)-C4ex+C5 where C1, C2, C3, C4, C5 are arbitrary constant, is

Question

The order of the differential equation whose general solution is given by y=(C1+C2)cos(x+C3)-C4ex+C5 where C1, C2, C3, C4, C5 are arbitrary constant, is (A) 5 (B) 4 (C) 3 (D) 2

Tardigrade Admin · Accepted Answer

The given equation can be written as y = Acos(x + C3) - Bex where A = C1 + C2 and B = C4eC5 Here, there are three independent variables, (A, B, C3). Hence, the differential equation will be of order 3.

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

$5$

$4$

$3$

$2$

The given equation can be written as
$y = A cos (x + C_{3}) - B e^{x}$
where $A = C_{1} + C_{2}$ and $B = C_{4} e^{C_{5}}$
Here, there are three independent variables,
$(A, B, C_{3})$ .
Hence, the differential equation will be of order $3$ .

Q. The order of the differential equation whose general solution is given by y=(C1​+C2​)cos(x+C3​)−C4​ex+C5​ where C1​, C2​, C3​, C4​, C5​ are arbitrary constant, is

5

4

3

2

The given equation can be written as y=Acos(x+C3​)−Bex where A=C1​+C2​ and B=C4​eC5​ Here, there are three independent variables, (A,B,C3​). Hence, the differential equation will be of order 3.

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

$5$

$4$

$3$

$2$

The given equation can be written as
$y = A cos (x + C_{3}) - B e^{x}$
where $A = C_{1} + C_{2}$ and $B = C_{4} e^{C_{5}}$
Here, there are three independent variables,
$(A, B, C_{3})$ .
Hence, the differential equation will be of order $3$ .