What is the solution for (dy)/(dx)= 1/x (y^2+0.2y) ?

The solution for (dy)/(dx)= 1/x (y^2+0.2y) is y=(0.2e^{(ln(x)+c_{1})/5})/(1-e^{(ln(x)+c_{1))/5}}

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(dy)/(dx)= 1/x (y^2+0.2y)

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

y = \frac{0.2 e ^{\frac{l n ( x ) + c _{1}}{5}}}{1 - e ^{\frac{l n ( x ) + c _{1}}{5}}}

Solution steps

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.2 y)

Solve separable ODE:

y = \frac{0.2 e ^{\frac{l n ( x ) + c _{1}}{5}}}{1 - e ^{\frac{l n ( x ) + c _{1}}{5}}}

y = \frac{0.2 e ^{\frac{l n ( x ) + c _{1}}{5}}}{1 - e ^{\frac{l n ( x ) + c _{1}}{5}}}

\int \frac{4 x ^{2} + 1}{4 x} d x

\int 3 x^{2} - 5 x + \frac{7}{x} + 2 e^{3} d x

\frac{\partial}{\partial x} (\frac{( x + y )}{x y})

x \to 2 + lim (x^{2} + 1)

y = 4 x - 3 x^{2}

What is the solution for (dy)/(dx)= 1/x (y^2+0.2y) ?
The solution for (dy)/(dx)= 1/x (y^2+0.2y) is y=(0.2e^{(ln(x)+c_{1})/5})/(1-e^{(ln(x)+c_{1))/5}}