The solution of differential equation `x^(2)=1 + (x/y)^(-1) (dy)/(dx) + ((x/y)^(-2)((dy)/(dx))^(2))/(2)+.....`

Answer

A

Explanation

`x^(2)=e^((x/y)^(-1)(dy)/(dx))=e^((y/x)(dy)/(dx))`
or `"ln "x^(2)=y/x(dy)/(dx)`
or `intx" ln "x^(2)dx=intydy`
Putting `x^(2)=t`, we get `2xdx=dt`
or `1/2 int " ln" t dt =y^(2)/2`
or `c+t" ln "t-t=y^(2)`
or `y^(2)=x^(2)" ln "x^(2)-x^(2)+c`