Question

Equation of the line: ( y=a x+b );
Distance from the line to origin: ( d=frac{|b|}{sqrt{a^{2}+1}}=1 rightarrow b=pm sqrt{a^{2}+1} )
So ( y=a x pm sqrt{a^{2}+1} rightarrow frac{d y}{d x}=frac{d}{d x}(a x pm sqrt{a^{2}+1}) rightarrow y^{prime}=a )
and ( y=y^{prime} x pm sqrt{y^{prime 2}+1} rightarrowleft(y-x y^{prime}right)^{2}=y^{prime 2}+1 )

# The differential equation for all the straight lines which are at a unit distance from the origin is Уt X1 [3011811626]

Solution