Question

The solution of the differential equation `dy/dx + y/x = 1 - x^3 + 4x` is ______ 

Options

• `xy = x^3/3 + 3/2 x^2 + 2x + c`

• `xy = x^3/3 + x^2 + x + c`

• `xy = x^2/2 - x^5/5 + 4 x^3/3 + c`

• `xy = x^2/2 + x^5/5 + 4 x^3/3 + c`

Answer 1

The solution of the differential equation `dy/dx + y/x = 1 - x^3 + 4x` is `underline(xy = x^2/2 - x^5/5 + 4 x^3/3 + c)`.

Explanation:

`dy/dx + y/x = 1 - x^3 + 4x`

Here, p = `1/x`, Q = 1 - x³ + 4x

∴ I.F. = `e^{int1/x dx} = e^{logx} = x`

∴ solution of the given equation is

y.x = `int(1 - x^3 + 4x) x dx + c`

⇒ xy = `intx dx - intx^4 dx + 4intx^2 dx + c`

⇒ `xy = x^2/2 - x^5/5 + 4 x^3/2 + c`