Question

The solution of the equation `dy/dx = (3x − 4y − 2)/(3x − 4y − 3)` is ______.

Options

• (x − y²) + c = log (3x − 4y + 1)

• x − y + c = log (3x − 4y + 4)

• (x − y + c) = log (3x − 4y − 3)

• x − y + c = log (3x − 4y + 1)

Answer 1

The solution of the equation `dy/dx = (3x − 4y − 2)/(3x − 4y − 3)` is x − y + c = log (3x − 4y + 1).

Explanation:

Hint: Put 3x − 4y = X

⇒ `3 − 4  dy/dx = (dX)/dx ⇒ dy/dx = 1/4(3 − (dX)/dx)`

⇒ `3/4 − 1/4 (dX)/dx = (X − 2)/(X − 3)`

⇒ `−1/4 (dX)/dx = (4X − 8 − 3(X − 3))/(4(x − 3))`

⇒ `−1/4 (dX)/dx`

⇒ `(X + 1)/(4 (X − 3))`