What is the solution for (y/x+9x)dx+(ln(x)-4)dy=0,x>0 ?

The solution for (y/x+9x)dx+(ln(x)-4)dy=0,x>0 is y=-(9x^2)/(2(ln(x)-4))+(c_{1})/(ln(x)-4)

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(y/x+9x)dx+(ln(x)-4)dy=0,x>0

(\frac{y}{x} + 9 x) d x + (ln (x) - 4) d y = 0, x > 0

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 4 )} + \frac{c _{1}}{ln ( x ) - 4}

Solution steps

(\frac{y}{x} + 9 x) d x + (ln (x) - 4) d y = 0

Solve linear ODE:

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 4 )} + \frac{c _{1}}{ln ( x ) - 4}

y = - \frac{9 x ^{2}}{2 ( ln ( x ) - 4 )} + \frac{c _{1}}{ln ( x ) - 4}

\int cos (ln (x)) ln (x) d x

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\frac{\partial}{\partial x} (4 - x^{2} - 2 y^{2})

What is the solution for (y/x+9x)dx+(ln(x)-4)dy=0,x>0 ?
The solution for (y/x+9x)dx+(ln(x)-4)dy=0,x>0 is y=-(9x^2)/(2(ln(x)-4))+(c_{1})/(ln(x)-4)