Determine a region of the xy -plane for which the given differential equation wo

Question

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point (x0, y0) in the region.style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">style="font-style: italic;">style="font-style: italic;">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">style="font-family: verdana, helvetica, sans-serif; font-size: 13px; line-height: 20px;">

xdx/dy = y

Explanation / Answer

x*dx=y*dy

x^2=y^2+c

c=constant of integration

putting (x0,y0)

we get c=x0^2-y0^2

so equation given

y=sqrt(x^2-x0^2+y0^2)

so the region of xy plane is given by

x^2-x0^2+y0^2>=0

x>=sqrt(x0^2-y0^2)

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