Question

The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is ______.

Options

• `e^(x - y) = x + 1`

• `e^(x + y) = x + 1`

• `e^x + e^y = x + 1`

• `e^(y - x) = x - 1`

Answer 1

The particular solution of `dy/dx = xe^(y - x)`, when x = y = 0 is `underlinebb(e^(x - y) = x + 1)`.

Explanation:

`dy/dx = xe^(y - x)`

∴ `int e^-y dy = intxe^-x dx`

∴ `e^-y = x * e^-x/-1 - int 1 * e^-x/-1 dx + c`

∴ `-e^-y = -xe^-x + e^-x/-1 + c`

∴ `e^-y = x/e^x + 1/e^x - c`

∴ `e^(x - y) = x + 1 - ce^x`

When x = y = 0, we get

1 = 1 – c          ∴ c = 0

∴ Particular solution is

`e^(x - y) = x + 1`