What is the solution for (y/x+9x)dx+(ln(x)-2)dy=0 ?

The solution for (y/x+9x)dx+(ln(x)-2)dy=0 is y=-(9x^2)/(2(ln(x)-2))+(c_{1})/(ln(x)-2)

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(y/x+9x)dx+(ln(x)-2)dy=0

(\frac{y}{x} + 9 x) d x + (ln (x) - 2) d y = 0

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

Solution steps

(\frac{y}{x} + 9 x) d x + (ln (x) - 2) d y = 0

Solve linear ODE:

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 2 )} + \frac{c _{1}}{ln ( x ) - 2}

What is the solution for (y/x+9x)dx+(ln(x)-2)dy=0 ?
The solution for (y/x+9x)dx+(ln(x)-2)dy=0 is y=-(9x^2)/(2(ln(x)-2))+(c_{1})/(ln(x)-2)