Question

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 $y=\left(c_{1}+c_{2}\right) \sin \left(x +c_{3}\right)+c_{4} e^{x+ c_{5}}$, is

• A. 3
• B. 5
• C. 4
• D. Not defined

Answer 1

Answer: (A)

General solution of differential equation is, $y=\left(C_{1}+C_{2}\right) \sin \left(x +C_{3}\right)+C_{4} e^{x+ C_{5}}$
Here solution is of form;
$y=A \sin \left(x +C_{3}\right)+B e^{x}$
${\left[\because C_{1}+C_{2}=A, C_{4} e^{c}=B\right]}$
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 $3$.