The solution of (y-3 x^2) d x+x d y=0 is | vedclass

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(C) Given the differential equation: $(y-3 x^2) d x+x d y=0$. Rearranging the terms, we get: $y d x-3 x^2 d x+x d y=0$. Grouping the terms $y d x$ and

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$y(x)=x^2+\frac{C}{x}$

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(C) Given the differential equation: $(y-3 x^2) d x+x d y=0$. Rearranging the terms, we get: $y d x-3 x^2 d x+x d y=0$. Grouping the terms $y d x$ and $x d y$, we have: $y d x+x d y=3 x^2 d x$. Recognizing the product rule for differentiation, $d(x y) = y d x + x d y$, the equation becomes: $d(x y) = 3 x^2 d x$. Integrating both sides: $\int d(x y) = \int 3 x^2 d x$. This yields: $x y = x^3 + C$. Dividing by $x$ (assuming $x 
eq 0$), we get the solution: $y = x^2 + \frac{C}{x}$.

The solution of $(y-3 x^2) d x+x d y=0$ is

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