Solution of the differential equation 3ydydx-2x-0 represents a family of

Given, 3ydydx+2x=0 ⇒ 3ydy +2xdx=0 (variable separable form) integrating we get, nbsp; 3y^22+2x^22=C2 2x^2+3y^2=C (C is a constant) ⇒ family of ellipses ...

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Engineering Mathematics

Variables Separable Method II(Equations Reducible to VS Form)

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Solution of the differential equation $3 y \frac{d y}{d x} + 2 x = 0$ represents a family of

ellipses

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Solution

The correct option is A ellipses
Given, $3 y \frac{d y}{d x} + 2 x = 0$

$\Rightarrow 3 y d y + 2 x d x = 0$ (variable separable form)

integrating we get,

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

$2 x^{2} + 3 y^{2} = C$

(C is a constant)

$\Rightarrow$ family of ellipses

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Solution of the differential equation 3ydydx+2x=0 represents a family of

The correct option is A ellipsesGiven, 3ydydx+2x=0 ⇒3ydy+2xdx=0 (variable separable form) integrating we get, 3y22+2x22=C2 2x2+3y2=C (C is a constant) ⇒ family of ellipses

Solution of the differential equation $3 y \frac{d y}{d x} + 2 x = 0$ represents a family of

The correct option is A ellipses
Given, $3 y \frac{d y}{d x} + 2 x = 0$

$\Rightarrow 3 y d y + 2 x d x = 0$ (variable separable form)

integrating we get,

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

$2 x^{2} + 3 y^{2} = C$

(C is a constant)

$\Rightarrow$ family of ellipses