What is a solution to the differential equation $\frac{d y}{d x} = \frac{2 x}{y}$ $dy/dx=(2x)/y$ ?

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What is a solution to the differential equation $\frac{d y}{d x} = \frac{2 x}{y}$ $dy/dx=(2x)/y$ ?

2 Answers

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Answer 1 · 2016-07-12T22:29:14

I found: $y = \pm \sqrt{2 x + c}$ $y=+-sqrt(2x+c)$

Explanation:

We can try separating and write:
$y d y = 2 x d x$ $ydy=2xdx$
then integrate:
$\int y d y = \int 2 x d x$ $intydy=int2xdx$
$\frac{y^{2}}{2} = x^{2} + c$ $y^2/2=x^2+c$
or:
$y^{2} = 2 x^{2} + c$ $y^2=2x^2+c$
and:
$y = \pm \sqrt{2 x^{2} + c}$ $y=+-sqrt(2x^2+c)$

Answer 2 · 2016-07-13T00:08:09

$y = \pm \sqrt{2 x^{2} + C}$ $y = pm sqrt( 2x^2 + C)$

Explanation:

$\frac{d y}{d x} = \frac{2 x}{y}$ $dy/dx=(2x)/y$

$y \ dy/dx=2x$

$int \ y \ dy/dx \ dx=int \ 2x \ dx$

$int \ y \ dy=int \ 2x \ dx$

$y^2/2=2 * x^2/2 + C$

$y^2/2 = x^2 + C$

$y^2 = 2x^2 + C$

$y = pm sqrt( 2x^2 + C)$

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What is a solution to the differential equation $\frac{d y}{d x} = \frac{2 x}{y}$ $dy/dx=(2x)/y$ ?

2 Answers

Explanation:

Explanation:

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What is a solution to the differential equation $\frac{d y}{d x} = \frac{2 x}{y}$ $dy/dx=(2x)/y$ ?