The solution of dydx-2x3y2 is-

The correct option is C y^3 x^2=c dydx= 2x 3y ^ 2 ⇒∫ 3y^2dy=∫2xdx+c →3y^33=2x^22+c → y^3 x^2=c ...

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Standard XII

Mathematics

Variable Separable Method

The solution ...

Question

The solution of $\frac{d y}{d x} = \frac{2 x}{3 y^{2}}$ is:

y^{3} + x^{2} = c

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y^{2} + x^{3} = c

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y^{3} - x^{2} = c

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y^{3} - x = c

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Solution

The correct option is C $y^{3} - x^{2} = c$
$\frac{d y}{d x} = \frac{2 x}{{3 y}^{2}}$

$\Rightarrow \int 3 y^{2} d y = \int 2 x d x + c$

$\to \frac{3 y^{3}}{3} = \frac{2 x^{2}}{2} + c$

$\to y^{3} - x^{2} = c$

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The solution of dydx=2x3y2 is:

The correct option is C y3−x2=cdydx=2x3y2⇒∫3y2dy=∫2xdx+c→3y33=2x22+c→y3−x2=c

The solution of $\frac{d y}{d x} = \frac{2 x}{3 y^{2}}$ is:

The correct option is C $y^{3} - x^{2} = c$
$\frac{d y}{d x} = \frac{2 x}{{3 y}^{2}}$

$\Rightarrow \int 3 y^{2} d y = \int 2 x d x + c$

$\to \frac{3 y^{3}}{3} = \frac{2 x^{2}}{2} + c$

$\to y^{3} - x^{2} = c$