Question 860108
{{{xy*(dy/dx)=y^2+4}}}
{{{(y*dy)/(y^2+4)=dx/x}}}
Substitute, {{{u=y^2+4}}}, {{{du=2y*dy}}}, {{{(1/2)du=y*dy}}}
{{{du/(2u)=dx/x}}}
{{{(1/2)ln(u)=ln(x)+C}}}
{{{ln(sqrt(u))=ln(x)+C}}}
{{{sqrt(u)=Cx}}}
{{{u=Cx^2}}}
{{{y^2+4=Cx^2}}}
{{{y^2=Cx^2-4}}}
Solve for C.
{{{0=C(1)^2-4}}}
{{{C-4=0}}}
{{{C=4}}}
{{{highlight(y^2=4(x^2-1))}}}