What is the solution for (dx)/(dy)=(xy^2+x)/(10y^2) ?

The solution for (dx)/(dy)=(xy^2+x)/(10y^2) is x=e^{1/10 (-1/y+y)+c_{1}}

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(dx)/(dy)=(xy^2+x)/(10y^2)

\frac{d x}{d y} = \frac{x y ^{2} + x}{10 y ^{2}}

x = e^{\frac{1}{10} (- \frac{1}{y} + y) + c_{1}}

Solution steps

\frac{d x}{d y} = \frac{x y ^{2} + x}{10 y ^{2}}

Solve separable ODE:

x = e^{\frac{1}{10} (- \frac{1}{y} + y) + c_{1}}

x = e^{\frac{1}{10} (- \frac{1}{y} + y) + c_{1}}

\frac{d y}{d x} = x y^{2}, y (- 3) = - \frac{1}{5}

(- 4 x y^{2} - 4 y) d x + (- 4 x^{2} y - 4 x) d y = 0

\frac{d V}{d t} = 1 - 0.4 \cdot V

y^{^{'}} = \frac{3 t ^{2} y}{y + 1}

\frac{d y}{d x} y^{2} - x^{3} = 28

What is the solution for (dx)/(dy)=(xy^2+x)/(10y^2) ?
The solution for (dx)/(dy)=(xy^2+x)/(10y^2) is x=e^{1/10 (-1/y+y)+c_{1}}