Question

Particular solution of differential equation `e^{dy/dx} = x:y(1) = 3; x > 0` is ______ 

Options

• 2y = x² + 5 

• y = x log x - x + 4

• logy = x² + 4

• y² = logx + 4

Answer 1

Particular solution of differential equation `e^{dy/dx} = x:y(1) = 3; x > 0` is y = x log x - x + 4.

Explanation:

`e^{dy/dx} = x`

⇒ `dy/dx = logx`

⇒ `intdy = intlogx dx`

⇒ y = logx.(x) - ∫dx + c

⇒ y = x logx - x + c

Since y(1) = 3, i.e., y = 3 when x = 1

∴ 3 = log 1 - 1 + c

⇒ c = 4

∴ y = x log x - x + 4