What is the solution of the differential equation $x d y + y d x = 0$

x y = c

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y = c x

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x + y = c

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x - y = c

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Solution

The correct option is C $x y = c$
Consider $x d y + y d x = 0$

$\Rightarrow x d y = - y d x$

$\Rightarrow \frac{1}{y} d y = - \frac{1}{x} d x$

Integrating both sides we get

$\Rightarrow l n | y | = - l n | x | + C$

$\Rightarrow l n | y | + l n | x | = C$

$\Rightarrow l n (| x | | y |) = C$

$\Rightarrow | x | | y | = e^{C}$

$\Rightarrow x y = e^{C}$

Let $e^{C} = c$ we get

$\Rightarrow x y = c$

Suggest Corrections

Similar questions

The general solution of the differential equation is

A. xy = C

B. x = Cy²

C. y = Cx

D. y = Cx²

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) $y = C x^{2}$

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

C

x d y + y d x = \frac{x d y - y d x}{x^{2} + y^{2}}

c

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

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