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`(x^(2)-y^(2))dx+2xy dy=0` |
Answer» `2xy dy = (y^(2)-x^(2))dx` `implies (dy)/(dx)=(y^(2)-x^(2))/(2xy)` `implies v+x(dv)/(dx)=(v^(2)x^(2)-x^(2))/(2x^(2)v)` माना `y = vx implies (dy)/(dx)=v+x(dv)/(dx)` `implies x(dv)/(dx)=(v^(2)-1)/(2v)-v=(-(1+v^(2)))/(2v)` `implies (2v)/(1+v^(2))dv=-(dx)/(x)` `implies int(2v)/(1+v^(2))dv=-int(dx)/(x)+logc` `implies log(1+v^(2))=-logx+logc` `implies 1+v^(2)=(c)/(x) implies x^(2)+v^(2)x^(2)=cx` `implies x^(2)+y^(2)=cx` |
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