If c1, c2, c3, c4, c5 are arbitrary constants, then the order of the differential equation whose general solution is y=(c1+c2) sin (x +c3)+c4 ex+ c5, is

Question

If c1, c2, c3, c4, c5 are arbitrary constants, then the order of the differential equation whose general solution is y=(c1+c2) sin (x +c3)+c4 ex+ c5, is (A) 3 (B) 5 (C) 4 (D) Not defined

Tardigrade Admin · Accepted Answer

General solution of differential equation is,

y = (C_{1} + C_{2}) sin (x + C_{3}) + C_{4} e^{x + C_{5}}

Here solution is of form;

y = A sin (x + C_{3}) + B e^{x}

[∵ C_{1} + C_{2} = A, C_{4} e^{c} = B]

So, there are 3 -arbitrary constants,

A_{1} C_{3}

and

B

Now, order of differential equation = number of arbitrary constants in general solution.
So, order of differential equation is

3

.

Q. If c1​,c2​,c3​,c4​,c5​ are arbitrary constants, then the order of the differential equation whose general solution is y=(c1​+c2​)sin(x+c3​)+c4​ex+c5​, is

3

5

4

Not defined

Q. If $c_{1}, c_{2}, c_{3}, c_{4}, c_{5}$ are arbitrary constants, then the order of the differential equation whose general solution is $y = (c_{1} + c_{2}) sin (x + c_{3}) + c_{4} e^{x + c_{5}}$ , is