Find the particular solution of the differential equation `e^xsqrt(1-y^2)dx+y/x dy=0,` given that `y=1` when `x=0`

Explanation

`e^xdx(sqrt(1-y^2))+ydy(1/x)=0`

`xe^xdxsqrt(1-y^2)+ydy=0`

`xe^xdx=((-y)dy)/sqrt(1-y^2)`

integrating both side

`intxe^xdx=int(-y)dy/sqrt(1-y^2)`

`intxe^xdx=x inte^xdx-intdx/dx*inte^xdxdx`

`xe^x-inte^xdx=xe^x-e^x`

`1/2t^(1/2)/(1/2)=sqrtt`

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