Which of the following statements on ordinary differential equations is/are true ?
(i) The number of arbitrary constants is same as the degree of the differential equation.
(ii) A linear differential equation can contain products of the dependent variable and its derivatives.
(iii) A particular integral cannot contains arbitrary constants.
(iv) By putting `v=(y)/(x)` any homogeneous first order differential equation transforms to variable separable form.

Options

A. (i) and (iii) only
B. (ii) and (iii) only
C. (iii) only
D. (i) and (iv) only

Answer

C

Explanation

The number of arbitrary constants in the solution of a differential equation is same as its order. So, statements (i) is not true. Statement (ii) is not true. However, statement (iii) is true. Some homogeneous differential equations reduce to variable separable form by putting `v=(y)/(x)`.