What is the general solution of the differential equation $x d y - y d x y^{2}$ ?

x = c y

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y^{2} = c x

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x + x y - c y = 0

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None of the above

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Solution

The correct option is D None of the above
$x d y - y^{3} d x = 0 r e a r r a n g i n g \frac{d x}{x} = \frac{d y}{y^{3}} i n t e g r a t i n g b o t h s i d e s ln x = \frac{y^{- 2}}{- 2} + c$

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Similar questions

y d x + (2 \sqrt{x y} - x) d y = 0

The general solution of the differential equation $\frac{y d x - x d y}{y} = 0$ is

a) $x y = C$

b) $x = C y^{2}$

c) $y = C x$

d) $y = C x^{2}$

(x + y) d x + x d y = 0

y d x - x d y = y^{2} tan (\frac{x}{y}) d x

C

The general solution of the differential equation is

A. xy = C

B. x = Cy²

C. y = Cx

D. y = Cx²

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