The general solution of the equation dy - dx - x 2 - y 2 is-

The correct option is D x^3 y^3=c #160; dy / dx = x ^ 2 / y ^ 2 ⇒ y ^ 2 dy= x ^ 2 dx Integrating both sides #160;∫ y ^ 2 dy =∫ x ^ 2 dx ⇒ y ^ 3 ...

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Standard XII

Mathematics

Variable Separable Method

The general s...

Question

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

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

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

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

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Solution

The correct option is D $x^{3} - y^{3} = c$
$\frac{d y}{d x} = \frac{x^{2}}{y^{2}} \Rightarrow y^{2} d y = x^{2} d x$
Integrating both sides
$\int y^{2} d y = \int x^{2} d x \Rightarrow \frac{y^{3}}{3} = \frac{x^{3}}{3} + \frac{c}{3}$
$\Rightarrow x^{3} - y^{3} = c$

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The general solution of the equation dydx=x2y2 is:

The correct option is D x3−y3=cdydx=x2y2⇒y2dy=x2dxIntegrating both sides∫y2dy=∫x2dx⇒y33=x33+c3⇒x3−y3=c

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

The correct option is D $x^{3} - y^{3} = c$
$\frac{d y}{d x} = \frac{x^{2}}{y^{2}} \Rightarrow y^{2} d y = x^{2} d x$
Integrating both sides
$\int y^{2} d y = \int x^{2} d x \Rightarrow \frac{y^{3}}{3} = \frac{x^{3}}{3} + \frac{c}{3}$
$\Rightarrow x^{3} - y^{3} = c$