Question

The differential equation whose solution is Ax² + By² = 1 where A and B are arbitrary constants is of ______.

पर्याय

• second order and second degree

• first order and second degree

• first order and first degree

• second order and first degree

Answer 1

The differential equation whose solution is Ax² + By² = 1 where A and B are arbitrary constants is of second order and first degree.

Explanation:

Ax² + By² = 1   ...(i)

Differentiate w.r.t. x

`Ax + By (dy)/(dx)` = 0  ...(ii)

Again differentiate w.r.t. x

`A + By (d^2y)/(dx^2) + B(dy/dx)^2` = 0  ...(iii)

From (ii) and (iii)

`x{-By(d^2y)/(dx^2) - B(dy/dx)^2} + By (dy)/(dx)` = 0

Dividing both sides by –B, we get

`xy (d^2y)/(dx^2) + x(dy/dx)^2 - y(dy)/(dx)` = 0

Therefore order 2 and degree 1.