The Solution of the differential equation ( 1 + x 3 ) d y d x + 3 x 2 y + cos 2 x - 1 = 0

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Solution

Q.
$The Solution of the differential equation (1 + x^{3}) \frac{d y}{d x} + 3 x^{2} y + \cos^{2} x - 1 = 0$

1 $y (1 + x^{3}) = \frac{x}{2} - \frac{1}{4} \sin 2 x + C$

2 $y (1 + x^{3}) = \frac{x}{2} + \frac{1}{4} \sin 2 x + C$

3 $y (1 + x^{3}) = \frac{x}{4} - \frac{1}{2} \sin 2 x + C$

4 $y (1 - x^{3}) = \frac{x}{2} - \frac{1}{4} \sin 2 x + C$

Ans.
(1)

$I . F = e^{\int (\frac{3 x^{2}}{1 + x^{3}}) d x} = 1 + x^{3}$

$y (1 + x^{3}) = \int \frac{1 - \cos (2 x)}{2} d x$

$y (1 + x^{3}) = \frac{x}{2} - \frac{1}{4} \sin 2 x + C$

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