Question

$( \frac{y}{x} + 6x)dx + ( ln(x) - 2)dy = 0$
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Answer 1

Hola :D

$y'\:+\frac{4}{x}y=x^3y^2,\:\quad y\left(2\right)=-1:\quad y=\frac{16}{x^4\left(-16\ln \left(x\right)-1+16\ln \left(2\right)\right)}$

Pasos:

$y'\:+\frac{4}{x}y=x^3y^2$

$=y^{1-n}\mathrm{\:y\:resolviendo\:}\frac{1}{1-n}v'+p\left(x\right)v=q\left(x\right)$

$y=\frac{16}{x^4\left(-16\ln\left(x\right)-1+16\ln\left(2\right)\right)}$

Saludos Nby