Question

The particular solution of the differential equation x dy + 2y dx = 0, when x = 2,y = 1 is ______.

Options

• xy = 4

• x²y = 4

• xy² = 4

• x²y² = 4

Answer 1

The particular solution of the differential equation x dy + 2y dx = 0, when x = 2,y = 1 is x²y = 4.

Explanation:

Given, x dy + 2y dx = 0

∴ `dy/dx + (2dx)/x` = 0

After integrating on both sides, we get

`int 1/y dy + 2int 1/x dx` = log C

`\implies` log y + 2 log x = log C

`\implies` yx² = C

If x = 2 then y = 1,

So, C = 1 × 2² = 4

Hence, particular solution will be x²y = 4.