Answer in Differential Equations

Given equation is incorrect

Correct equation is,

“y^2+x^2p^2-2xyp=4”

“(y-xp)^2=2^2”

“to y-xp=2”

“to y-xdfrac{dy}{dx}=2”

“to y-2=xdfrac{dy}{dx}”

“to dfrac{dy}{y-2}=dfrac{dx}{x}”

Integrating Both the sides

“to int dfrac{dy}{y-2}=intdfrac{dx}{x}” ‘

“therefore log(y-2)=logx+logc”

“to y-2=xc”

“to y=xc+2”

For general solution ,

as y=xc+2

or y-xc=2

Squaring on both sides

“to (y-xc)^2=2^2”

“to y^2+x^2c^2-2xyc=4\”

Subtract “c^2” on both sides

“to y^2+x^2c^2-2xyc-c^2=4-c^2\nto y^2-2xyc+c^2(x^2-1)=m^2” ( where “m^2=4-c^2” )

For SS

Let calculate value of constant at (0,0)

“to 0+c^2(-1)=m^2\nc^2=-m^2”

So SS is

“to y-0+c^2(-1)=m^2\nto y-c^2=m^2\nto y+m^2=m^2”

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