What is the solution for (y/x+3x)dx+(ln(x)-2)dy=0 ?

The solution for (y/x+3x)dx+(ln(x)-2)dy=0 is y=-(3x^2)/(2(ln(x)-2))+(c_{1})/(ln(x)-2)

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(y/x+3x)dx+(ln(x)-2)dy=0

(\frac{y}{x} + 3 x) d x + (ln (x) - 2) d y = 0

y = - \frac{3 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

Solution steps

(\frac{y}{x} + 3 x) d x + (ln (x) - 2) d y = 0

Solve linear ODE:

y = - \frac{3 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

y = - \frac{3 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

\int \frac{x ^{2} - 2 x}{x ^{3} - 3 x ^{2}} d x

- 3 t (6 t^{3} - 1)^{8}

\int_{0}^{π} x sin (x) d x

\frac{d}{d x} ((- 2 x^{2} - 2 x + 3)^{5})

\int cos (x) sin (x) cos^{2} (x) + 1 d x

What is the solution for (y/x+3x)dx+(ln(x)-2)dy=0 ?
The solution for (y/x+3x)dx+(ln(x)-2)dy=0 is y=-(3x^2)/(2(ln(x)-2))+(c_{1})/(ln(x)-2)