Question

The solution of the differential equation x(e^y - 1)dy + (x³ - 1)e^y dx = 0 is ______.

विकल्प

• `y+e^-y=logx-x^3/3+c`

• `y-e^-y=logx-x^3/3+c`

• `y+e^-y=logx+x^3/3+c`

• `y-e^-y=logx+x^3/3+c`

Answer 1

The solution of the differential equation x(e^y - 1)dy + (x³ - 1)e^y dx = 0 is `underline(y+e^-y=logx-x^3/3+c)`.

Explanation:

x(e^y - 1)dy + (x³ - 1)e^y dx = 0

⇒ x(e^y - 1)dy = (1 - x³)e^y dx

Integrating on both sides, we get

`int(e^y-1)/e^y dy=int(1-x^3)/x dx+c`

`=>int 1dy-inte^-y dy = int 1/x dx - int x^2 dx +c`

`=>y+e^-y=logx-x^3/3+c`