The solution of x-2y3dy-dx - y is where c is arbitrary constant

Dx/dy 1/y x = 2y^2 This is linear equation taking y as independent variable. Here, I.F. =e^ ∫1/ydy = e^ log y = 1/y ∴ solution is x 1/y = ∫1/y 2y^2 dy + c ⇒x ...

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Standard XIII

Mathematics

Solving Linear Differential Equations of First Order

The solution ...

Question

The solution of $(x + 2 y^{3}) (\frac{d y}{d x}) = y$ is (where c is arbitrary constant)

x = y^{3} + c y

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x = y^{3} - c y

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y = y^{3} - c y

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y = y^{3} + c y

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Solution

The correct option is B $x = y^{3} - c y$
$\frac{d x}{d y} - \frac{1}{y} x = 2 y^{2}$
This is linear equation taking y as independent variable.
Here, I.F. $= e^{- \int \frac{1}{y} d y} = e^{- l o g y} = \frac{1}{y}$
$∴$ solution is x $\frac{1}{y} = \int \frac{1}{y} 2 y^{2} d y + c$
$\Rightarrow \frac{x}{y} = y^{2} + c \Rightarrow x = y^{3} + c y$

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The solution of (x+2y3)(dydx)=y is (where c is arbitrary constant)

The correct option is B x=y3−cydxdy−1yx=2y2 This is linear equation taking y as independent variable. Here, I.F. =e−∫1ydy=e−logy=1y ∴ solution is x 1y=∫1y2y2dy+c ⇒xy=y2+c⇒x=y3+cy

The solution of $(x + 2 y^{3}) (\frac{d y}{d x}) = y$ is (where c is arbitrary constant)