Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut’s form by using the substitution X=x2, Y=y2 where p=$\frac{dy}{dx}$.

Question

Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut’s form by using the substitution X=x2, Y=y2  where p=$\frac{dy}{dx}$.

TuteeHUB · Accepted Answer

$x^2 = cy^2 – \frac{1}{2c+1}$

TuteeHUB · Answer

$y^2 = x + \frac{c}{c+1}$

TuteeHUB · Answer

$y^2 = cx^2 – \frac{2c}{c+1}$

TuteeHUB · Answer

$x^2 = cy^2 – \frac{1}{2c+1}$

TuteeHUB · Answer

$x^2 = y^2 + \frac{c}{2c+2}$

1.	Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut’s form by using the substitution X=x2, Y=y2 where p=\(\frac{dy}{dx}\).
A.	\(y^2 = x + \frac{c}{c+1}\)
B.	\(y^2 = cx^2 – \frac{2c}{c+1}\)
C.	\(x^2 = cy^2 – \frac{1}{2c+1}\)
D.	\(x^2 = y^2 + \frac{c}{2c+2}\)
Answer» C. \(x^2 = cy^2 – \frac{1}{2c+1}\)

Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut’s form by using the substitution X=x2, Y=y2 where p=\(\frac{dy}{dx}\).

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