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

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

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

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

y = e^{- \frac{1}{x} + c_{1}} x^{2}

Solution steps

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

Solve separable ODE:

y = e^{- \frac{1}{x} + c_{1}} x^{2}

y = e^{- \frac{1}{x} + c_{1}} x^{2}

(1 - y) e^{y} y^{^{'}} + \frac{y ^{2}}{x ln ( x )} = 0

2 x \frac{d y}{d x} = cos^{2} (y), y (0) = 2

\frac{d y}{d x} = e^{5 x - 5 y}

y^{^{'}} = x + 2 x y

3 x^{2} y^{2} d x + 2 x^{3} y d y = 0, y (1) = 2

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