What is the solution for 5xydx-ln^8(y)dy=0 ?

The solution for 5xydx-ln^8(y)dy=0 is y=e^{\sqrt[9]{(45x^2+c_{1})/2}}

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5xydx-ln^8(y)dy=0

5 x y d x - ln^{8} (y) d y = 0

y = e^{9 \frac{45 x ^{2} + c _{1}}{2}}

Solution steps

5 x y d x - ln^{8} (y) d y = 0

Solve separable ODE:

y = e^{9 \frac{45 x ^{2} + c _{1}}{2}}

y = e^{9 \frac{45 x ^{2} + c _{1}}{2}}

y^{^{'}} = \frac{1}{3} y

\frac{d y}{d x} y = u^{2} - 2 u, u = \frac{1}{x ^{2}}

3 = \frac{π}{12} \frac{d}{d t} ((h (t))^{3})

2 sin (3 x) sin (2 y) d y = 3 cos (3 x) cos (2 y) d x

7 x y \frac{d y}{d x} = 3, y > 0, x > 0

What is the solution for 5xydx-ln^8(y)dy=0 ?
The solution for 5xydx-ln^8(y)dy=0 is y=e^{\sqrt[9]{(45x^2+c_{1})/2}}