What is the solution for ((2x)/y)dy+((2ln(5y)+1)/x)dx=0 ?

The solution for ((2x)/y)dy+((2ln(5y)+1)/x)dx=0 is y=(e^{(e^{\frac{1+2c_{1}x)/x}-1)/(2)}}{5}

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((2x)/y)dy+((2ln(5y)+1)/x)dx=0

(\frac{2 x}{y}) d y + (\frac{2 ln ( 5 y ) + 1}{x}) d x = 0

y = \frac{e ^{\frac{e ^{\frac{1 + 2 c _{1} x}{x}} - 1}{2}}}{5}

Solution steps

(\frac{2 x}{y}) d y + (\frac{2 ln ( 5 y ) + 1}{x}) d x = 0

Solve separable ODE:

y = \frac{e ^{\frac{e ^{\frac{1 + 2 c _{1} x}{x}} - 1}{2}}}{5}

y = \frac{e ^{\frac{e ^{\frac{1 + 2 c _{1} x}{x}} - 1}{2}}}{5}

sin (t) cos (x) d t + sin (x) cos (t) d x = 0

\frac{d y}{d x} = e^{2 y}

x^{^{'}} = e^{- x}

\frac{d y}{d x} + y = 6 x^{2} y

y^{2} \frac{d y}{d x} = 3 x^{2} (y^{3} - 2)

What is the solution for ((2x)/y)dy+((2ln(5y)+1)/x)dx=0 ?
The solution for ((2x)/y)dy+((2ln(5y)+1)/x)dx=0 is y=(e^{(e^{\frac{1+2c_{1}x)/x}-1)/(2)}}{5}