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I need to solve this differential equation. YWhat I'm looking for is a way to simplify this equation. Can anybody give me hints/tricks to understand the following equation better:

$xy'(\cos(2x^3)\cos(x)-\sin(2x^3)\sin(x)) - $ $y(6x^3+x)\sin(2x^3+x)$ $+(12x^3+2x)\sin(2x^3+x)=0$

Ultimately I want to seperate variables and integrate to solve for $y(x)$

Thanks for your help :)

Edit: Please If you can help me solve this differential equation, any help would be appreciated :)

thanks

2 Answers 2

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Note that : $\cos(2x^3)\cos(x)−\sin(2x^3)\sin(x) = \cos(2x^3+x)$

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It seems to me that two first term of the equation: $xy'(\cos(2x^3)\cos(x)-\sin(2x^3)\sin(x)) - y(6x^3+x)\sin(2x^3+x)$ is somehow a part of total differential of $xy(\cos(2x^3+x))$ Since $d\left(x\cos(2x^3+x)y\right)=x\cos(2x^3+x)y'+y\left(\cos(2x^3+x)-(6x^3+x)\sin(2x^3+x)\right)$

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    @amWhy: I become refreshed whenever you wish me that Amy. Thanks :-)2013-04-06