Question

The general solution of the differential equation `dy/dx=sqrty/sqrtx` is ______.

Options

• `logsqrty=logsqrtx+C`

• `sqrty+sqrtx=C`

• `sqrty-sqrtx=C`

• `logsqrty+logsqrtx=C`

Answer 1

The general solution of the differential equation `dy/dx=sqrty/sqrtx` is `bbunderline(sqrty-sqrtx=C)`.

Explanation:

`dy/dx=sqrty/sqrtx`

`int1/sqrtydy=int1/sqrtxdx`

`inty^(-1/2)dy=intx^(-1/2)dx`

`y^(1/2)/(1/2)=x^(1/2)/(1/2)dx`

`y^(1/2)/(1/2)=x^(1/2)/(1/2)+C`

`2sqrty=2sqrtx+C`

`sqrty=sqrtx+C/2`

`sqrty=sqrtx+C`

∴ `sqrty-sqrtx=C`