Question

The general solution of the differential equation y dx – x dy = 0 is ______.

Options

• xy = C

• x = Cy²

• y = Cx

• y = Cx²

Answer 1

The general solution of the differential equation y dx – x dy = 0 is y = Cx.

Explanation:

y dx – x dy = 0

⇒ y dx – x dy = 0

⇒ `(dy)/y = (dx)/x`

⇒ `int (dy)/y = int (dx)/x + logK, K > 0`

⇒ log |y| = log |x| + log K

⇒ log |y| = log |x| K

⇒ |y| = |x| K

⇒ y = ± Kx

⇒ y = Cx