The integrating factor of the differential equation x -3 y 2 dy - dx - y isA-B- x-1C- 1-x2D- 1-y2

The correct option is B 1/y(x + 3y^2)dy/dx = y ⇒dx/dy = x/y + 3y ⇒dx/dy x/y = 3y Integrating factor nbsp; = e^∫ 1/y dy nbsp;= nbsp; nbsp;e^ ln y = ...

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Standard XII

Mathematics

nth Term of A.P

The integrati...

Question

The integrating factor of the differential equation $(x + 3 y^{2}) \frac{d y}{d x} = y$ is

\frac{1}{x}

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\frac{1}{y}

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\frac{1}{x^{2}}

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\frac{1}{y^{2}}

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Solution

The correct option is B $\frac{1}{y}$
$(x + 3 y^{2}) \frac{d y}{d x} = y \Rightarrow \frac{d x}{d y} = \frac{x}{y} + 3 y \Rightarrow \frac{d x}{d y} - \frac{x}{y} = 3 y$
Integrating factor
$= e^{\int - \frac{1}{y} d y} = e^{- ln y} = \frac{1}{y}$

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The Integrating Factor (IF) of the differential equation $x \frac{d y}{d x} - y = 2 x^{2}$ is
(a) $e^{- x}$
(b) $e^{- y}$
(c) $\frac{1}{x}$
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The integrating factor of the differential equation (x+3y2)dydx=y is

The correct option is B 1y(x+3y2)dydx=y⇒dxdy=xy+3y⇒dxdy−xy=3y Integrating factor =e∫−1y dy=e−lny=1y

The integrating factor of the differential equation $(x + 3 y^{2}) \frac{d y}{d x} = y$ is

The correct option is B $\frac{1}{y}$
$(x + 3 y^{2}) \frac{d y}{d x} = y \Rightarrow \frac{d x}{d y} = \frac{x}{y} + 3 y \Rightarrow \frac{d x}{d y} - \frac{x}{y} = 3 y$
Integrating factor
$= e^{\int - \frac{1}{y} d y} = e^{- ln y} = \frac{1}{y}$