Question

The general solution of the differential equation ydx – xdy = 0; (Given x, y > 0), is of the form

(Where 'c' is an arbitrary positive constant of integration)

Options

• xy = c

• x = cy²

• y = cx

• y = cx²

Answer 1

y = cx

Explanation:

ydx – xdy = 0

`\implies (ydx - xdy)/y^2` = 0

`\implies d(x/y)` = 0

`\implies` x = `1/c y`

`\implies` y = cx.

Answer 2

y = cx

Explanation:

ydx – xdy = 0

`\implies` ydx = xdy

`\implies dy/y = dx/x`; on integrating `int dy/y = int dx/x`

log_e |y| = log_e |x| + log_e |c|

Since x, y, c > 0, we write log_e y = log_e x + log_e c

`\implies` y = cx.