Question

If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = ______.

Options

• 1

• 4

• 3

• 2

Answer 1

If m and n are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and X-axis as its axis, then mn - m + n = 3.

Explanation:

Equation of family of parabolas with focus at (0, 0) and X-axis as axis is y² = 4a(x + a)  ......(i)

Differentiating (i) w.r.t. x, we get

`2y ("d")/("d"x)` = 4a  ......(ii)

Substituting (ii) in (i), we get

y² = `2y ("d"y)/("d"x)(x + y/2 ("d"y)/("d"x))`

⇒ y = `2x ("d"y)/("d"x) + y(("d"y)/("d"x))^2`

∴ order = m = 1, degree = n = 2

Now, mn – m + n = 1(2) – 1 + 2 = 3