Question

Solution of differential equation `xdy/dx - y = x^3` is ______ 

Options

• y = logx + `x^2/2 + a`

• y = `x^3/2 + ax`

• y = x² + ax

• None of these

Answer 1

Solution of differential equation `xdy/dx - y = x^3` is `underline(y = x^3/2 + ax)`.

Explanation: 

`xdy/dx - y = x^3`

⇒ `dy/dx - y/x = x^2`

∴ I.F. = `e^{int1/xdx} = e^{-logx} = 1/x`

∴ solution of the given equation is

`y/x = intx^2. 1/xdx + a`

⇒ `y/x = x^2/2 + a ⇒ y = x^3/2 + ax`