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The question is to solve $x\frac{\mathrm{d} y}{\mathrm{d} x}+3y=x^3y^2$.

I have found the homogenous solution $y_h = c_1 x^{-3}$

I am stuck at finding the particular solution. I am familiar with variation of parameters(which involve Wronskian and just $r(x)$ in RHS ) and solution by undetermined coefficients

Please do as well suggest any necessary reading required for the same

Soham

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    The original equation is the form of [Bernoulli's equation](http://m.cliffsnotes.com/study_guide/Bernoullis-Equation.topicArticleId-19736,articleId-19715.html). This suggests the substitution $w=y^{1-3}$ to reduce the equation to linear in $w$.2012-09-12
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    Much thanks. I had been at my wits end, and now I realize the answer was just there under my nose. Much thanks.2012-09-12
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    Voted to close it2012-09-12
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    Why? There's nothing wrong with question--it's well-written, polite and shows effort. If only every question here was like this one.2012-10-19

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