Question

Solution of differential equation `e^(x - 2y) = dy/dx` is ______.

Options

• 2e^x – e^2y = c

• e^x – e^2y = c

• 2e^x + e^2y = c

• e^2x – e^y = c

Answer 1

Solution of differential equation `e^(x - 2y) = dy/dx` is 2e^x – e^2y = c.

Explanation:

`e^(x - 2y) = dy/dx`

`\implies e^x/e^(2y) = dy/dx`

∴ e^xdx = e^2ydy

∴ `int e^x dx = int e^(2y)dy`

∴ e^x = `e^(2y)/2 + c_1`   

∴ 2e^x – e^2y = c   ....(c = 2c₁)